(Note: This is my best understanding of this subject from what I have heard, but I don’t guarantee it is without error.)
I recently delved into the confusing subject which is the history of the church movement that I grew up in and was involved in for most of my life. The church I grew up in is a Christian Church. It seems to me and probably anyone on the outside, that all churches (at least which aren’t a part of a different religion) would be Christian Churches, and I imagine that was part of the original idea in this confusing label. To be fair, up through even my parent’s generation, denominations were a lot more important to people. Saying that one was a part of a Christian Church I imagine stuck out more for the fact that one was not a Baptist or Presbyterian or Catholic, etc.
But now days with a multitude of various flavors of denominations and nondenominational churches, and with those designations meaning less to people, it seems the label of Christian Church is confusing. There is one more additional reason why this is a problem. The original idea was to get away from denominations and divisions, and instead just be Christian. However, while the Christian Church isn’t a denomination in the sense of having a hierarchical structure, it does seem to have a clear sense of which churches are in and out. It’s for this reason that I often refer to it as a nondenominational denomination.
Now for a bit of the history. The Christian Church came out of the Restoration Movement (not to be confused with the Reformation), which came about at the time of the Second Great Awakening. Part of the values of the Restoration Movement were to get away from denominationalism and try to be closer to the new testament church.
For various reasons, two different sides of this movement grew apart and were listed separately by the 1906 census. According to my sources, the main reason was that, while before the Civil War essentially all the churches of this movement were rural and could not afford instruments, afterwards, the churches in the North began to use instruments while the churches in the South could not afford them due to the poor state of the South after the war. As is common for people to do, since the churches of the South were in that position, they ended up developing a doctrine as to why instruments should not be used in worship. Most of these churches located in the South were known as Churches of Christ, with the parenthetical notation “(non-instrumental)” sometimes added to differentiate them from the Churches of Christ in the North.
Churches in the North were known as (independent) Christian Churches, Churches of Christ, or sometimes Disciples. Through the mid twentieth century, another division grew in the churches in the North. Some within the movement became theologically liberal. Those who were more conservative initially resisted, but later began a separate convention (the North American Christian Convention in 1927) after being ignored. The latter conservative churches are known as (independent) Christian Churches or Churches of Christ, while the former more liberal churches use the label Disciples of Christ and have adopted a more denominational like structure (1968).
Are you confused yet? There are presently Christian Churches/Churches of Christ, Disciples of Christ, and Churches of Christ non-instrumental. The Disciples of Christ and Churches of Christ (non-instrumental) split earlier, but Christian Churches/Churches of Christ and Churches of Christ (non-instrumental) are apparently more similar than different, and are apparently working toward reuniting to some degree.