“Fellowship” is the preferred term because it more appropriately describes the activity involved, and relegates it to close-knit gatherings of family and friends. Don’t you fellowship in family reunions, but still attend your own churches? Do you consider your family reunions a “church”?
Even so, it can definitely be called the church of Christ by definition of that term as well, even if they are not organized as a corporate church structure:
Behold, this is my doctrine—whosoever repenteth and cometh unto me, the same is my church. Whosoever declareth more or less than this, the same is not of me, but is against me; therefore he is not of my church. And now, behold, whosoever is of my church, and endureth of my church to the end, him will I establish upon my rock, and the gates of hell shall not prevail against them. And now, remember the words of him who is the life and light of the world, your Redeemer, your Lord and your God. Amen. (D&C 10:67-70).
There is no need for another corporate church structure:
True religion, when it is present on the earth, always existed in a community of believers. If we do not have community then we cannot be willing to mourn with those that mourn. We cannot comfort those that stand in need of comfort. We cannot stand as a witness to one another of God at all times and of all places. We cannot bear one another’s burdens so they may be light, as is required by the gospel and the covenant of baptism. None of this can be done without fellowship between believers. However, we do not need a new corporate church. The only thing we need is a community to fellowship one another. Whether called a ‘community,’ or ‘fellowship’ or ‘society’ it does not matter. Legal entities, whenever formed, become prey to the law. Men can gain control over legal entities. Legal entities are vulnerable to sycophants willing to do whatever is required to show they are desperately submissive to those in power. Hierarchies invite abuse. Aspiring men can always corrupt whatever is organized on the earth. (Denver Snuffer, Preserving the Restoration, pp. 504-505, see also the crucial and illuminating footnotes on those pages).
What we refer to as the “LDS Church” is a legal entity. Fellowships are “churches” in the generic use of the term. When you read D&C 10, do you consider Christ was referring to an earthly legal entity, or the generic use of the term applied to the conditions he specified?
Consider also, though, that the fellowships are not fully organized as the church of Christ might be, seeing that much of the labor needed in the fellowships is at this time decidedly left to the angels to sort out later (see D&C 20, D&C 42, and JST Matthew 13:39-44). Therefore, a portion of the organizational boundaries for our “church” encompasses the powers of heaven beyond the veil. On this side of the veil in the fellowships, we don’t necessarily exclude others by reference to church articles, nor do we necessarily exclude others from taking the sacrament. We are promised in scripture the following, when all necessary church politics will be sorted out by those angels and Christ Himself:
And Jesus answered and spake unto them again by parables, and said, The kingdom of heaven is like unto a certain king, which made a marriage for his son, And sent forth his servants to call them that were bidden to the wedding: and they would not come. Again, he sent forth other servants, saying, Tell them which are bidden, Behold, I have prepared my dinner: my oxen and my fatlings are killed, and all things are ready: come unto the marriage. But they made light of it, and went their ways, one to his farm, another to his merchandise: And the remnant took his servants, and entreated them spitefully, and slew them. But when the king heard thereof, he was wroth: and he sent forth his armies, and destroyed those murderers, and burned up their city. Then saith he to his servants, The wedding is ready, but they which were bidden were not worthy. Go ye therefore into the highways, and as many as ye shall find, bid to the marriage. So those servants went out into the highways, and gathered together all as many as they found, both bad and good: and the wedding was furnished with guests. And when the king came in to see the guests, he saw there a man which had not on a wedding garment: And he saith unto him, Friend, how camest thou in hither not having a wedding garment? And he was speechless. Then said the king to the servants, Bind him hand and foot, and take him away, and cast him into outer darkness; there shall be weeping and gnashing of teeth. For many are called, but few are chosen. (Matthew 22:1-14; see also Luke 14:15-24).
As Christ says, we don’t destroy the law or the prophets (3 Nephi 12:17) or any church articles, but we seek to live the true intent of them, and not one jot or tittle shall pass away, but shall all be fulfilled in their due time, even if in our limited mortal perspective things look out of place, or out of order. God wills it, and so we must invite all to the wedding feast from the highways and the byways without judgment. These small and simple things will have a great impact, and we refuse to strain at the gnats, because thereby we might swallow the camel (Matthew 23:24). The doctrine of Christ is our priority now. It is useless to build up a superstructure that has no heart and soul. It becomes an empty shell, and the revelations that the early Saints pressed Joseph for were largely premature for them, or missing the mark concerning God’s priorities for the Restoration. But, they were given what they asked for. Even so, all things, including the elaborate church structure contained in the D&C, testify of Christ, and have their place in the Gospel (see Moses 6:63).
As before explained, the “doctrine” in the Doctrine and Covenants was the Lectures on Faith which were removed by the LDS Church in 1920. The “covenants” were not all covenants between God and man, but also covenants between themselves as a church. The early Latter-day Saints believed “in the same organization that existed in the Primitive Church”. So do we, but we do not covenant with each other to be so governed in the fellowships. There are no offices. We covenant to pattern in a way that allows the fulness to return, which is less administrative outwardly, and more administered in one’s heart, with the law written on people’s hearts (2 Corinthians 3:3). It is a higher standard befitting friends and family–if we can be so called, and if we avoid contention significantly enough. If not, we devolve into the need for offices and presiding authorities.
The following statement from Denver Snuffer is instructive: “An unchanging God has an unchanging gospel. Rather than taking pride in our ordinances, we should view ourselves in our lost and fallen state. Rebuild faith through repentance. Once the inward part has been cleansed there will be time to worry about the outward part.” (Denver Snuffer, Preserving the Restoration, p. 230).
Who is a wise and a just servant? (see JST, Luke 12:41-57).