The following are some conclusions that were drawn as a result of our pondering, which were forwarded to me.  Significant material was drawn from the works of Hyrum Andrus, former dean of religious studies at BYU.

After a lot of thought, and putting together things I have read and heard, here is what I believe.

I believe that the ritual comprises the actions and the use of spoken words when we make a covenant and receive the promise of a blessing. Then as a result of our obedience to the law, and the enactment of the ritual, we are eligible to have the ordinance made effective in our lives – usually a gradual rather than an instantaneous occurrence, but often with some profoundly “quantum leap” moments on the way.

My basis for this idea comes from a couple of things that Hyrum Andrus says in his classes. First of all, he states that the Catholic Church is really big into “rites.” As an example, they believe that if a wicked man is dying, and a priest can get to him and administer the “last rites” then the man will not go to hell. Similarly, if a baby dies before having the rite of baptism, the baby will go to hell. Protestants have taken this  in the other direction. A “born again” Christian will usually be able to tell you when and where he was when he was “saved” because he accepted Christ in his heart. Hyrum then goes on to say the our Church has both – the rite and the blessing (ordinance?) that goes with it.

My note: It is my understanding that there is a big focus on the rites in the Catholic Church. However, I believe they do recognize a difference between rites and “sacraments” (which I would say are roughly equivalent to our ordinances). If I understand Catholic theology on this (and I don’t know if I do), rites are the things humans do, while Sacraments involve an action on God’s part as well — a bestowal of “grace” upon the person performing the act.

Another great point that Andrus makes, that I have not heard from anyone else, is that when Joseph first wrote the Articles of Faith, the third one stated “…by obedience to the laws and ordinances of the Gospel.” Then the 4th Article read “We believe that the first ordinances of the gospel are: first, Faith in the Lord Jesus Christ; second, Repentance;…” You will notice that the fourth one did not contain the word “principles.” Joseph is on record as referring to faith and repentance as ordinances, and at other times referring to them as principles, and in the early 1900′s (according to Andrus’ research) the word principles was added to the 4th Article of Faith. Now, since we like everything simple and lined up, we teach that faith and repentance are principles and baptism and laying on of hands for the Gift of the Holy Ghost are ordinances. Not wrong, but also not all of what Joseph was trying to convey.

Hyrum then goes on to say that faith is both a principle and an ordinance. It has the beauty of being an ordinance that we can perform on ourselves in the privacy of our own homes, with no one else needed.

Now, in true Hyrum-style, he does not go on to explain exactly how one performs this ordinance, and I think this is very instructive. There is no ritual required for us to receive the ordinances of faith and repentance. However, I do think the Sacrament is part of the ritual of repentance (perhaps faith also) and this is where I am able to get my mind around the rituals of the temple and how they connect with the ordinances we are supposed to receive there.

If I think about doing proxy work, it is easy for me to understand that I am performing the rituals. Hands are placed on my head, I say words, physical contact is made and actions are performed. However, I know that if the person I am proxy for does not accept the ordinance, then the work I have done is not efficacious. So, what happens in a live ordinance, when a person is baptized, or attends the temple for the first time, or is sealed? The ritual has been performed and is the person is (ritually) prepared for the ordinance to become a reality in his/her life. Once again, this usually happens gradually, especially when we are baptized as children and recieve our endowment as relatively young men and women. However, I am beginning to be able to attest that if we strive for the Spirit in our lives, and if we are hungering and thirsting after knowledge, and with the capacity to compress time a bit (at my age five years seems short) we will see that there are some huge leaps that we can and will take at times.

I wish that we were taught more, and had more conversations in our gospel doctrine classes, about spiritual rebirth. We should be teaching that it does not come by just living the Law, or by performing the Rite, but that the ordinance comes when we are born anew to spiritual things.

I would like to thank my friend for contributing these great insights on this question.  The follwing are some notes from research I did on the topic. Please note that although I have had some training in Greek and Hebrew, I do not consider myself an expert by any means and am open to any suggestions/corrections that any of you might have.

Rite vs. Ordinance

Dictionary definition of ordinance:

1 a : a Christian rite (as baptism or the Eucharist) that is believed to have been ordained by Christ and that is held to be a means of divine grace or to be a sign or symbol of a spiritual reality b : a religious rite or observance comparable to a Christian sacrament

An authoritative command or order.
A custom or practice established by long usage.
A Christian rite, especially the Eucharist.
A statute or regulation, especially one enacted by a city government.

Dictionary definition of rite:

1 a: a prescribed form or manner governing the words or actions for a ceremony b: the ceremonial practices of a church or group of churches2: a ceremonial act or action <initiation rites>3: a division of the Christian church using a distinctive liturgy
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According to Mormon.org, an ordinance is:

A sacred rite or ceremony performed by the power of the priesthood and intended to bless God’s children. Some ordinances, such as baptism, are essential for salvation. Other ordinances, such as administering to the sick, constitute gifts from God to His children which are not essential for salvation. Many ordinances have symbolic meaning.
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Rite is only mentioned twice in Book of Mormon (Alma 43:45, 44:5) and is not mentioned in D&C or PofGP. It is also not mentioned in New Testament.
Old Testament:
RSV Exodus 12:24 You shall observe this rite as an ordinance for you and for your sons for ever.

rite = rb”åD”h; = the word, matter, thing, speech

ordinance = qx’ = something prescribed, work, task, obligation, required amount, statute, law, order

Other Translations of this verse:

BBE Exodus 12:24 And you are to keep this as an order to you and to your sons for ever.

DRA Exodus 12:24 Thou shalt keep this thing as a law for thee and thy children for ever.

KJV Exodus 12:24 And ye shall observe this thing for an ordinance to thee and to thy sons for ever.

NAB Exodus 12:24 “You shall observe this as a perpetual ordinance for yourselves and your descendants.

NAS Exodus 12:24 “And you shall observe this event as an ordinance for you and your children forever.

NIV Exodus 12:24 “Obey these instructions as a lasting ordinance for you and your descendants.

NJB Exodus 12:24 You will observe this as a decree binding you and your children for all time,

NRS Exodus 12:24 You shall observe this rite as a perpetual ordinance for you and your children.
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NAB Exodus 29:1 “This is the rite you shall perform in consecrating them as my priests. Procure a young bull and two unblemished rams.

rite = rb”åD”h; = the word, matter, thing, speech

Other translations of this verse:

BBE Exodus 29:1 This is what you are to do to make them holy, to do the work of priests to me: Take one young ox and two male sheep, without any mark on them,

DRA Exodus 29:1 And thou shalt also do this, that they may be consecrated to me in priesthood. Take a calf from the herd, and two rams without blemish,

KJV Exodus 29:1 And this is the thing that thou shalt do unto them to hallow them, to minister unto me in the priest’s office: Take one young bullock, and two rams without blemish,

NAS Exodus 29:1 “Now this is what you shall do to them to consecrate them to minister as priests to Me: take one young bull and two rams without blemish,

NIV Exodus 29:1 “This is what you are to do to consecrate them, so they may serve me as priests: Take a young bull and two rams without defect.

NJB Exodus 29:1 ‘This is what you will do to them, to consecrate them to my priesthood. Take one young bull and two rams without blemish;
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NJB Exodus 13:5 and when Yahweh has brought you into the country of the Canaanites…, flowing with milk and honey, which he swore to your ancestors that he would give you, then you must observe this rite in the same month.

rite = hd”îbo[]h = work, labor, service (esp. cultic service)

Other translations of this verse:

BBE Exodus 13:5 And it will be that, when the Lord takes you into the land of the Canaanite and the Hittite and the Amorite and the Hivite and the Jebusite, the land which he made an oath to your fathers that he would give you, a land flowing with milk and honey, you will do this act of worship in this month.

DRA Exodus 13:5 And when the Lord shall have brought thee into the land of the Chanaanite, and the Hethite, and the Amorrhite, and the Hevite, and the Jebusite, which he swore to thy fathers that he would give thee, a land that floweth with milk and honey, thou shalt celebrate this manner of sacred rites in this month.

KJV Exodus 13:5 And it shall be when the LORD shall bring thee into the land of the Canaanites…, which he sware unto thy fathers to give thee, a land flowing with milk and honey, that thou shalt keep this service in this month.

NAS Exodus 13:5 “And it shall be when the LORD brings you to the land of the Canaanite…, which He swore to your fathers to give you, a land flowing with milk and honey, that you shall observe this rite in this month.

NIV Exodus 13:5 When the LORD brings you into the land of the Canaanites…,– the land he swore to your forefathers to give you, a land flowing with milk and honey– you are to observe this ceremony in this month:

NRS Exodus 13:5 When the LORD brings you into the land of the Canaanites…, which he swore to your ancestors to give you, a land flowing with milk and honey, you shall keep this observance in this month.

RSV Exodus 13:5 And when the LORD brings you into the land of the Canaanites…, which he swore to your fathers to give you, a land flowing with milk and honey, you shall keep this service in this month.
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KJV Exodus 13:10 Thou shalt therefore keep this ordinance in his season from year to year.

ordinance = hQ”ïxuh = due, fixed times, statutes (esp. divine)

Other translations of this verse:

BBE Exodus 13:10 So let this order be kept, at the right time, from year to year.

DRA Exodus 13:10 Thou shalt keep this observance at the set time from days to days.

NAB Exodus 13:10 Therefore, you shall keep this prescribed rite at its appointed time from year to year.

NIV Exodus 13:10 You must keep this ordinance at the appointed time year after year.

NJB Exodus 13:10 You shall observe this law at its appointed time, year by year.

RSV Exodus 13:10 You shall therefore keep this ordinance at its appointed time from year to year.

Note: In the various translations above, we see the Hebrew being translated as, among other terms, both “ordinance” and “rite.”
KJV Exodus 12:17 And ye shall observe the feast of unleavened bread; for in this selfsame day have I brought your armies out of the land of Egypt: therefore shall ye observe this day in your generations by an ordinance for ever.

ordinance =  hQ”ïxuh= due, fixed time, statute (esp. divine), ordinance, enactment

BBE Exodus 12:17 So keep the feast of unleavened bread; for on this very day I have taken your armies out of the land of Egypt: this day, then, is to be kept through all your generations by an order for ever.

DRA Exodus 12:17 And you shall observe the feast of the unleavened bread: for in this same day I will bring forth your army out of the land of Egypt, and you shall keep this day in your generations by a perpetual observance.

NAB Exodus 12:17 “Keep, then, this custom of the unleavened bread. Since it was on this very day that I brought your ranks out of the land of Egypt, you must celebrate this day throughout your generations as a perpetual institution.

NAS Exodus 12:17 ‘You shall also observe the Feast of Unleavened Bread, for on this very day I brought your hosts out of the land of Egypt; therefore you shall observe this day throughout your generations as a permanent ordinance.

NIV Exodus 12:17 “Celebrate the Feast of Unleavened Bread, because it was on this very day that I brought your divisions out of Egypt. Celebrate this day as a lasting ordinance for the generations to come.

NJB Exodus 12:17 You must keep the feast of Unleavened Bread because it was on that same day that I brought your armies out of Egypt. You will keep that day, generation after generation; this is a decree for all time.

RSV Exodus 12:17 And you shall observe the feast of unleavened bread, for on this very day I brought your hosts out of the land of Egypt: therefore you shall observe this day, throughout your generations, as an ordinance for ever.

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KJV Isaiah 24:5 The earth also is defiled under the inhabitants thereof; because they have transgressed the laws, changed the ordinance, broken the everlasting covenant.
ordinance =  qx’ = something prescribed, work, task, obligation, required amount, statute, law, order, ordinance

Other translations of this verse:

BBE Isaiah 24:5 The earth has been made unclean by those living in it; because the laws have not been kept by them, the orders have been changed, and the eternal agreement has been broken.

DRA Isaiah 24:5 And the earth is infected by the inhabitants thereof: because they have transgressed the laws, they have changed the ordinance, they have broken the everlasting covenant.

NAB Isaiah 24:5 The earth is polluted because of its inhabitants, who have transgressed laws, violated statutes, broken the ancient covenant.

NIV Isaiah 24:5 The earth is defiled by its people; they have disobeyed the laws, violated the statutes and broken the everlasting covenant.

NJB Isaiah 24:5 The earth is defiled by the feet of its inhabitants, for they have transgressed the laws, violated the decree, broken the everlasting covenant.

RSV Isaiah 24:5 The earth lies polluted under its inhabitants; for they have transgressed the laws, violated the statutes, broken the everlasting covenant.
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KJV Ezekiel 46:14 And thou shalt prepare a meat offering for it every morning, the sixth part of an ephah, and the third part of an hin of oil, to temper with the fine flour; a meat offering continually by a perpetual ordinance unto the LORD.

ordinance = qx’ = something prescribed, work, task, obligation, required amount, statute, law, order, ordinance

Other translations of this verse:

BBE Ezekiel 46:14 And you are to give, morning by morning, a meal offering with it, a sixth of an ephah and a third of a hin of oil dropped on the best meal; a meal offering offered to the Lord at all times by an eternal order.

DRA Ezekiel 46:14 And he shall offer the sacrifice for it morning by morning, the sixth part of ephi: and the third part of a bin of oil be mingled with the fine hour: a to the Lord by ordinance continual and everlasting.

NAS Ezekiel 46:14 “Also you shall provide a grain offering with it morning by morning, a sixth of an ephah, and a third of a hin of oil to moisten the fine flour, a grain offering to the LORD continually by a perpetual ordinance.

NIV Ezekiel 46:14 You are also to provide with it morning by morning a grain offering, consisting of a sixth of an ephah with a third of a hin of oil to moisten the flour. The presenting of this grain offering to the LORD is a lasting ordinance.

NJB Ezekiel 46:14 Every morning in addition he must offer an oblation of one-sixth of an ephah and one-third of a hin of oil, for mixing with the flour. This is the oblation to Yahweh, a perpetual decree, fixed for ever.

NRS Ezekiel 46:14 And he shall provide a grain offering with it morning by morning regularly, one-sixth of an ephah, and one-third of a hin of oil to moisten the choice flour, as a grain offering to the LORD; this is the ordinance for all time.

RSV Ezekiel 46:14 And he shall provide a cereal offering with it morning by morning, one sixth of an ephah, and one third of a hin of oil to moisten the flour, as a cereal offering to the LORD; this is the ordinance for the continual burnt offering.
New Testament:

KJV Hebrews 9:1 Then verily the first covenant had also ordinances of divine service, and a worldly sanctuary.

ordinances = dikaiw,mata = righteous deeds, regulations, requirements, commandments, laws

Other translations of this verse:

BBE Hebrews 9:1 Now the first agreement had its rules of worship, and a holy order.

DRA Hebrews 9:1 The former indeed had also justifications of divine service, and a worldly sanctuary.

NAB Hebrews 9:1 Now (even) the first covenant had regulations for worship and an earthly sanctuary.

NAS Hebrews 9:1 Now even the first covenant had regulations of divine worship and the earthly sanctuary.

NIV Hebrews 9:1 Now the first covenant had regulations for worship and also an earthly sanctuary.

NJB Hebrews 9:1 The first covenant also had its laws governing worship and its sanctuary, a sanctuary on this earth.

NRS Hebrews 9:1 Now even the first covenant had regulations for worship and an earthly sanctuary.

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KJV Hebrews 9:10 Which stood only in meats and drinks, and divers washings, and carnal ordinances, imposed on them until the time of reformation.

ordinances =  dikaiw,mata = righteous deeds, regulations, requirements, commandments

Other translations of this verse:

BBE Hebrews 9:10 Because they are only rules of the flesh, of meats and drinks and washings, which have their place till the time comes when things will be put right.

DRA Hebrews 9:10 And divers washings, and justices of the flesh laid on them until the time of correction.

NAB Hebrews 9:10 but only in matters of food and drink and various ritual washings: regulations concerning the flesh, imposed until the time of the new order.

NIV Hebrews 9:10 They are only a matter of food and drink and various ceremonial washings– external regulations applying until the time of the new order.

NJB Hebrews 9:10 they are rules about outward life, connected with food and drink and washing at various times, which are in force only until the time comes to set things right.

NRS Hebrews 9:10 but deal only with food and drink and various baptisms, regulations for the body imposed until the time comes to set things right.

RSV Hebrews 9:10 but deal only with food and drink and various ablutions, regulations for the body imposed until the time of reformation.
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KJV Ephesians 2:15 Having abolished in his flesh the enmity, even the law of commandments contained in ordinances; for to make in himself of twain one new man, so making peace;

ordinances = do,gmasin = (dogmas), decrees, commandments, ordinances, requirements
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KJV Luke 1:6 And they were both righteous before God, walking in all the commandments and ordinances of the Lord blameless.

ordinances = dikaiw,masin = righteous deeds, regulations, requirements, commandments

Other translations of this verse:

BBE Luke 1:6 They were upright in the eyes of God, keeping all the rules and orders of God, and doing no wrong.

DRA Luke 1:6 And they were both just before God, walking in all the commandments and justifications of the Lord without blame.

NAB Luke 1:6 Both were righteous in the eyes of God, observing all the commandments and ordinances of the Lord blamelessly.

NAS Luke 1:6 And they were both righteous in the sight of God, walking blamelessly in all the commandments and requirements of the Lord.

NIV Luke 1:6 Both of them were upright in the sight of God, observing all the Lord’s commandments and regulations blamelessly.

NJB Luke 1:6 Both were upright in the sight of God and impeccably carried out all the commandments and observances of the Lord.

NRS Luke 1:6 Both of them were righteous before God, living blamelessly according to all the commandments and regulations of the Lord.

RSV Luke 1:6 And they were both righteous before God, walking in all the commandments and ordinances of the Lord blameless.
Preliminary Conclusions on Uses of “Rite” and “Ordinance”

The word “rite” in the scriptures appears almost exclusively in the Old Testament, with a mere two instances outside, in the Book of Mormon. The word comes as a translation of various Hebrew words, including davar (which is a very general word that can mean “thing, word, speech, saying” and avodah (which usually means “work, service”). Many translations choose to translate these words using other terms besides “rite,” including thing, this, this thing, decree, instructions, event (for davar) and act of worship, sacred rite, service, ceremony, observance (for avodah). Overall, while “rite” can have other meanings, the term seems to refer most often to ritual acts of worship. However, it is not a necessary translation of the Hebrew originals and seems to simply be preferred by some translators, drawing on the term’s familiar use in religious context.

The word “ordinance” is a more common word, being found in all books of scripture. In the Old Testament, it most frequently is a translation of the Hebrew hoq, which has the general meaning of “a divine decree, or command” and which can be translated as “something prescribed, work, task, obligation, required amount, statute, law, order, ordinance.” It is a more specific word than “rite,” but can be applied to more situations than is customary in the LDS church. It seems to have the general meaning of “divine requirement or obligation.”

In the New Testament, the Greek word dikaiomatos carries more of a “righteous deed” meaning, but is related to rules and commandments given by God. It is specifically used to describe the carnal commandments and rites of the Law of Moses.

In some cases, the same word in Hebrew is translated as both “rite” and “ordinance” by different translators, indicating that the ideas are fairly interchangeable. I haven’t found much difference in meaning between the two terms, except that rite seems to be a more generic word than ordinance. My overall impression is that an ordinance = a rite that is set in order by the Lord/the Church. In the LDS Church, the performance of an ordinance would require the priesthood.
Selected passages from LDS writings:

No ordinance of the Gospel can be performed acceptably to God or with afficacy to man except by its authority and power, and certainly there is no ordinance or rite instituted by the Almighty in the great plan of redemption which is not essential to the salvation or exaltation of his children. Therefore, where the Melchisedec or Holy Priesthood does not exist, there can be no true Church of Christ in its fulness.

(Contributor, vol. 10 (November 1888-October 1889), Vol. X. June, 1889. No. 8. 307.)
Baptism anciently. Perhaps here we may remark that baptism is a sacred ordinance, or a rite, as old as the Gospel, itself.

(George Reynolds and Janne M. Sjodahl, Commentary on the Book of Mormon, edited and arranged by Philip C. Reynolds, 7 vols. [Salt Lake City: Deseret Book Co., 1955-1961], 7: 145.)

Twelve marble pillars, extending from floor to ceiling in the Baptistry, are arranged in groups of three in each of the four corners of the room. These are further emblematic of the twelve sons of Jacob or the twelve apostles of the Lord. The room is furnished with four large bronze chandeliers of most modern and artistic design, is finished in Tennessee marble and oak, and has an elaborately ornamented plaster ceiling about 30 feet in height. Appropriate seats are provided for those in waiting, also a desk at the font, and a place for those who witness the baptism-by-immersion ordinance, for each rite of this holy house is attested by witnesses.

(Hugh B. Brown, Continuing the Quest [Salt Lake City: Deseret Book Co., 1961], 293.)

The baptism of repentance for the remission of sins] There is no other true baptism. This holy rite is a cleansing ordinance; it is the sole ordained way for accountable people to free themselves from sin.

(Bruce R. McConkie, Doctrinal New Testament Commentary, 3 vols. [Salt Lake City: Bookcraft, 1965-1973], 1: .)

As time passed during the early Christian centuries, many strange and foreign practices crept into the Christian baptism, transforming the holy ordinance into a rite which was distinctly different from the original Gospel revelation.

(Milton R. Hunter, The Gospel through the Ages [Salt Lake City: Stevens & Wallis, Inc., 1945], 203 – 204.)

During the first four thousand years of the earth’s temporal existence, thousands and tens of thousands of sacrifices were made unto the God of Israel. Each and every sacrifice, from the first to the last, was but a miniature model, a prototype of the last and great sacrifice offered up by Jesus. In each rite, consecration, and ordinance; in every solemnity, ritual, and ceremony; in all observances, duties, and ministrations; indeed, in the entire system of sacrifices and offerings given of God in all ages, the spiritually alert can identify aspects of Jesus’ atonement. In short, all sacrifices were designed to be “a similitude of the sacrifice of the Only Begotten of the Father” (Moses 5:7).

(Joseph Fielding McConkie and Donald W. Parry, A Guide to Scriptural Symbols [Salt Lake City: Bookcraft, 1990], .)

[Believers in] God have always commemorated the great atoning sacrifice of our Lord and Savior by a holy ordinance. Originally this rite was that of sacrifice, which was practiced down to the advent of the Only Begotten Son of God. At the death of the Master, however, the ancient law was fulfilled in His “infinite and eternal sacrifice.” He, therefore, gave to mortals a new ordinance known as the “Sacrament of the Lord’s Supper,” otherwise termed the “Holy Eucharist.”

(The Common Source of Religious Truth, Improvement Era, 1940, Vol. Xliii. March, 1940. No. 3. .)

Mere performance of the formal rite or ordinance of baptism, standing alone and without full compliance with the law on the part of the converted persons, does not put the Lord’s cleansing power into operation. No blessing ever accrues to men except as a result of full compliance with the law upon which its receipt is predicated

(Bruce R. McConkie, Mormon Doctrine, 2d ed. [Salt Lake City: Bookcraft, 1966], 296.)

An ordinance can be either a law (teaching, directive, or commandment) or an act (ritual, rite, or ceremony). Ordinance acts are just one important subcategory within the ordinance laws of the gospel. In general LDS practice, however, the term ordinance usually refers to the act, such as baptism, laying on of hands, sealing, and so on.

(Victor L. Ludlow, Principles and Practices of the Restored Gospel [Salt Lake City: Deseret Book Co., 1992], 286.)

When it is fully understood, however, that the marriage ceremony performed in the House of the Lord-though performed by worthy priesthood bearers granted sacred sealing powers-is a conditional ordinance, a rite whose eventual blessings are contingent upon the faithfulness (in years to come) of the participants,…

(Robert L. Millet and Kent P. Jackson, eds., Studies in Scripture, Vol. 1: The Doctrine and Covenants [Salt Lake City: Deseret Book Co., 1989], 518 – 519.)

This is a ritualized thing. Remember, ancient society was sacral. Everything they did was a rite, an ordinance. If they went to war, it was an ordinance. When they came back, it was an ordinance. And everything we do is an ordinance. It’s ritualized. We don’t hold it sacred necessarily, but say a football game. We follow rules and ordinances and colors and procedures-everything as if it had been orchestrated since the year one. This elaborate [procedure] of a football game is a rite. It’s symbolic, one color against the other color, and one gets the most points. All these people come, sit around and look at it, and take sides. They cheer together in unison.

(Hugh Nibley, Teachings of the Book of Mormon–Semester 1: Transcripts of Lectures Presented to an Honors Book of Mormon Class at Brigham Young University, 1988–1990 [Provo: Foundation for Ancient Re 41.)

Baptism is an eternal ordinance, an everlasting rite, a continuing requirement in God's kingdom, and it was practiced by the Jews before John ever came on the scene to minister for a short season among men. He was no more the originator of baptism than he was of faith or repentance or sacrifice or any of the other laws in the which he believed or the ordinances in which he participated. It is true that the Jews today no longer perform baptisms, just as they have ceased their sacrificial rites, but it was not so anciently, and it had not been so from the beginning

(Sperry Symposium Voices of Old Testament Prophets: The 26th Annual Sidney B. Sperry Symposium [Salt Lake City: Deseret Book Co., 1997], 182 – 183.)

An ordinance is a religious rite or ceremony based upon the law or commandment of God.

(Hyrum L. Andrus, Doctrinal Commentary on the Pearl of Great Price [Salt Lake City: Deseret Book Co., 1967], 244.)

Conclusion

The terms “rite” and “ordinance” seem to be used fairly synonymously most of the time. Most sources indicate that an ordinance is a religious rite.

“Rite” seems to be a more generic term for religious acts/rituals. When rites and ordinances are used in the same phrase, they are usually equated. Sometimes “rite” seems to be used somewhat pejoratively when compared to ordinance. Perhaps ordinances are simply a specific/special rite commanded by God, and a rite is a ritual act of worship.

Note: I apologize if some items in this post appear to be cut off — the system is acting up and arbitrarily cutting some lines before they’re finished.