Our covenants are validated by the ordinances and the ordinances are validated by our keeping the covenants. The sacrament is a renewal and affirmation of both.
Even though the words of the two sacrament blessings are similar, their intent is quite different. The blessing on the bread is a three part covenant. The blessing on the water is an affirmation that we are keeping those covenants.
“Witness” can mean to make a covenant or to take an oath, and the context of the two prayers suggests the word is intended to mean different things in the different prayers. “That” is a powerful conjunction that creates a dependent sequence of ideas.
The blessing on the bread reads:
O God, the Eternal Father, we ask thee in the name of thy Son, Jesus Christ, to bless and sanctify this bread to the souls of all those who partake of it; that they may eat in remembrance of the body of thy Son,
And witness [to covenant] unto thee, O God, the Eternal Father,
.  that they are willing to take upon them the name of thy Son,
.  and [ that they are willing to] always remember him
.  and [ that they are willing to] keep his commandments which he has given them;
that they may always have his Spirit to be with them. Amen
The blessing on the water reads:
O God, the Eternal Father, we ask thee, in the name of thy Son, Jesus Christ, to bless and sanctify this wine to the souls of all those who drink of it, that they may do it in remembrance of the blood of thy Son, which was shed for them;
. that they may witness [to take an oath] unto thee, O God, the Eternal Father,
. that they DO always remember him,
that they may have his Spirit to be with them. Amen.
In 3 Nephi 18 the resurrected Savior administers the sacrament to the Nephites, and in conjunction with that he also instituted a formal covenant with them. There are two correspond scriptures in the Book of Mormon that discuss this. One is Mosiah 5 where King Benjamin officiates as the people make a similar covenant. The other is Moroni 4 and 5 where the sacrament prayers are given verbatim. The covenants made by the people of King Benjamin and the ones in 3 Nephi are incorporated as an integral part of those prayers.
The Lord’s instructions to the Nephites includes the terms and objectives of the covenant. He said:
7 And this shall ye do in remembrance of my body, which I have shown unto you. And it shall be a testimony unto the Father that ye do always remember me. And if ye do always remember me ye shall have my Spirit to be with you.
8 And it came to pass that when he said these words, he commanded his disciples that they should take of the wine of the cup and drink of it, and that they should also give unto the multitude that they might drink of it.
9 And it came to pass that they did so, and did drink of it and were filled; and they gave unto the multitude, and they did drink, and they were filled.
10 And when the disciples had done this, Jesus said unto them: Blessed are ye for this thing which ye have done, for this is fulfilling my commandments, and this doth witness unto the Father that ye are willing to do that which I have commanded you.
11 And this shall ye always do to those who repent and are baptized in my name; and ye shall do it in remembrance of my blood, which I have shed for you, that ye may witness unto the Father that ye do always remember me. And if ye do always remember me ye shall have my Spirit to be with you (3 Nephi 18:7-11).
In Mosiah 5 the people spoke in unison and said:
5 And we are willing to enter into a covenant with our God to do his will, and to be obedient to his commandments in all things that he shall command us, all the remainder of our days, that we may not bring upon ourselves a never-ending torment, as has been spoken by the angel, that we may not drink out of the cup of the wrath of God.
To which the king responded:
6 And now, these are the words which king Benjamin desired of them; and therefore he said unto them: Ye have spoken the words that I desired; and the covenant which ye have made is a righteous covenant.
7 And now, because of the covenant which ye have made ye shall be called the children of Christ, his sons, and his daughters; for behold, this day he hath spiritually begotten you; for ye say that your hearts are changed through faith on his name; therefore, ye are born of him and have become his sons and his daughters.
8 And under this head ye are made free, and there is no other head whereby ye can be made free. There is no other name given whereby salvation cometh; therefore, I would that ye should take upon you the name of Christ, all you that have entered into the covenant with God that ye should be obedient unto the end of your lives.
9 And it shall come to pass that whosoever doeth this shall be found at the right hand of God, for he shall know the name by which he is called; for he shall be called by the name of Christ.
10 And now it shall come to pass, that whosoever shall not take upon him the name of Christ must be called by some other name; therefore, he findeth himself on the left hand of God.
11 And I would that ye should remember also, that this is the name that I said I should give unto you that never should be blotted out, except it be through transgression; therefore, take heed that ye do not transgress, that the name be not blotted out of your hearts.
12 I say unto you, I would that ye should remember to retain the name written always in your hearts, that ye are not found on the left hand of God, but that ye hear and know the voice by which ye shall be called, and also, the name by which he shall call you (Mosiah 5:5-12).
As King Benjamin explains, to take upon oneself the name of Christ is to “become his sons and his daughters.” When we are adopted into a new family we take the family name as our own. But the terms of the adoption covenant mean more than that. An adopted child has the full rights of inheritance. So to take upon us the name of Christ is to lay claim to all the blessings implied by the family relationship.
The blessing on the bread is a reiteration of that covenant. Like all covenants it has two parts: the promises of the first party and the promises of the second.
For our part, we—
“witness unto thee, O God, the Eternal Father, that they are willing [that is the operative word] to take upon them the name of thy Son, and [that they are willing to] always remember him, and [that they are willing to] keep his commandments which he hath given them,”
For God’s part, his promise is
“that they may always have his Spirit to be with them (Moroni 4:3).
The blessing on the water is different from that. It is an assertion and an evidence that we are actually keeping the covenants we just made:
that they may do it in remembrance of the blood of thy Son, which was shed for them; that they may witness … that they do [“do” is the operative word here] always remember him,
Through that assertion we lay claim to the fulfillment of the Father’s part of the covenant:
“that they may have his Spirit to be with them” (Moroni 5:2).
Notwithstanding the fact that we take the sacrament weekly, and that many, especially the children, do not understand what the words say, there is noting trivial suggested in its frequent repetition. When the words of the covenants in the blessing on the bread are understood to represent a renewing of all of the covenants we have made, including the temple covenants; and the words of the blessing on the water asserts that we are keeping all of those covenants, then we begin to understand power represented in those ordinances.
It is little wonder the Savior warned:
28 And now behold, this is the commandment which I give unto you, that ye shall not suffer any one knowingly to partake of my flesh and blood unworthily, when ye shall minister it;
29 For whoso eateth and drinketh my flesh and blood unworthily eateth and drinketh damnation to his soul….(3 Nephi 18:28-29).