This is all speculation on my part, but my very basic understanding is that a Requiem (a.k.a. a "funeral Mass") is celebrated with the body present, and the various rites associated with the Requiem are used. A "memorial Mass" is celebrated without the body present, and, IIRC, would fall under the various rubrics associated with a votive Mass. As there is no body present, the introductory rites of the NO would be used, i.e., sign of the cross and greeting, penitential rite from one of the options, no Gloria, readings either of the day, or if the day is a feria, from the readings appointed for funerals, no creed, no commendation prayers, etc. I would think that the "inserts" for the commemoration of the dead in the Eucharistic prayer would be OK as long as the Mass were not being celebrated in observance of an obligatory memorial appointed in the Ordo.

(Rant:) Really I think that the use of a "memorial Mass" in place of a proper Requiem constitutes one of the many abuses introduced into the liturgical life of the Church as a means of "not offending" the surviving family members of the deceased, especially if the deceased was devout and observant and the survivors are fallen away or lapsed.

Every time this question comes up it makes me realize that, as a convert to the Faith with no immediate family that truly understands my commitment to orthodoxy and orthopraxis, it is of utmost importance that I spell out exactly how I want the rites to be observed. Otherwise it'll be all down to "On Eagle's Wings" and some awful cantor catterwauling their way through "Shepherd Me, O God" for the responsorial psalm. Ugh.

Oh, B is with the body absent (hopefully present with the Lord)

In the practice of my parish, the casket is sprinkled and covered with the pall as soon as it arrives--either right in time for the funeral mass, or earlier if the visitation will be at the church. If it happens earlier, the funeral starts with the opening prayer, and then goes right to the liturgy of the word. We did have a priest from Nigeria who would sprinkle instead of incense at the song of farewell but our current priests only use insence there.

Assuming you are referring to the Ordinary Form of the Roman Rite, there are two authorities on the rites for funerals, in addition to the Missal itself: the Latin editio typica called Ordo Exsequiarum (1969) and, in the US and other places where it is approved, the Order of Christian Funerals [OCF] (1989).

The Roman Missal provides essentially three Mass formularies for the dead: the funeral (or exsequial Mass), the anniversary Mass, and the daily Mass for the dead. The funeral Mass is generally celebrated on the day of death or burial and is not repeated. Normally the body is present. The rites at the entrance of the church (Greeting, Sprinkling with Holy Water, optional placing of pall and other Christian Symbols) are adaptations of the Roman Ritual by the Conferences of Bishops. In the Latin typical edition there is provision for a procession from the home of the deceased to the church, in which case the Entrance Chant is sung as the procession enters the church and the priest and ministers go to the altar. The body is placed in the customary position (the faithful facing the altar, sacred ministers facing the people), the Book of Gospels or volume of Sacred Scriptures or a Cross may be placed on it, and candles may be placed around the bier, or the paschal candle may be placed at the head of the deceased. Then Mass begins as usual with the Introductory Rites. This holds true even if the procession is omitted and the priest meets the mourners who accompany the body at the door of the church. He greets them warmly, sprinkles the body with holy water (where it is the custom) and may say one or more prayers from the Ritual.

It is interesting to note that there is not one mention of a pall in the Roman Rite and the color for funerals and Masses for the Dead is left to the Episcopal Conferences to determine. Even in the US, where the white pall is commonplace, the OCF makes it optional. Also the typical edition allows for the omission of the Alleluia before the Gospel and at the end of the processional chants, even during the Easter Season, if pastoral reasons dictate. In the US the color for requiems is black, violet, or white, at the discretion of the priest-celebrant.

The Final Commendation and Farewell (in the usus antiquior called Absolution over the Catafalque) is only celebrated when the body is present; it may take place in the church following the Prayer after Communion of the Funeral Mass, replacing the Concluding Rites, or at the cemetery in conjunction with the Committal. Otherwise it is omitted, and Mass concludes with the Blessing and Dismissal.

Recently, in planning the music for the funeral of a family member, I was told emphatically by the parish's Director of Worship that the Kyrie could not be sung, even though only the ashes were present and there was no procession and rites at the door. The priest came out from the sacristy, said a few words of welcome and proceeded to the Collect. That seemed to me to have contradicted the rubrics.

By the way, at the funeral that I referred to above, the parts of the Mass that we were allowed to sing in Latin (the priest insisted on an English Responsorial Psalm and Alleluia Verse) were from the Missa pro defunctis by Giammateo Asola (c. 1532-1609). All who attended the Mass reacted positively to the music and were able to enter into the action of the liturgy through active listening. I wonder why we insist on encouraging people to sing hymns at funerals when often the mourners are not able to sing for reasons that are obvious.

One further note: the texts of the psalms in the Ordo Exsequiarum are from the Clementine Vulgate, but the musical settings in the Graduale Romanum use the Neo-Vulgata. Curious that the monks of Solesmes opted for the latter.