As far as the history of the Restoration Movement (Church of Christ, Christian Churches, Disciples of Christ) the wikipedia article is about as good as one can easily find. The two original movements, the Stone movement and theCampbell movement also have good wikipedia articles, so I’ll be brief about the early history and speak more to the differences between the three churches today.
Four men were instrumental in the development of the Restoration Movement, Thomas Campbell and his son, Alexander, Barton Stone, and Walter Scott. Stone had been a Presbyterian minister and began calling for reform against the denominationalism of the Presbyterian church. during this time he became convinced that adherence to the Westminster and Augsberg Confessions was unscriptural, along with Calvinist doctrine, which Stone considered to be the chief cause of the divisiveness in American churches of the time. The Campbells emerged from the Baptist church with a primitivist view of returning to First Century Christianity, as outlined solely in the NT, as much as possible. Walter Scott was a Presbyterian minister, wound up joining the Campbells in the Mahoning Baptist Association, and subsequently leaving the Baptists with the Campbells, with Scott bringing an emphasis on evangelism that the Campbells and Stone were weaker on. All four men were influenced by Enlightenment thinkers and wanted their movement to be characterized by freedom of belief in non-essential theology issues. Their early mottos were to “speak where Scripture speaks, and be silent where Scripture is silent” and “In essentials, Unity; in non-essentials, Liberty; and in all things, Charity.”
At that point in time, their doctrine was characterized by Baptism of believers by immersion for the remission of sins and weekly observance of the Lord’s Supper. All five points of Calvinist TULIP were preached against regularly. There was a very strong millennial belief in the Restoration movement, with a belief that the Millennium would only occur once denominations had fallen away and the church was once again unified.
Today, the main differences between the Church of Christ and the Christian Churches is in the use of instrumental music in worship, with the CoC holding that* a capella* singing is the only scriptural music, since there are no mentions of musical intruments being used in worship in the NT. Other than that, their doctrines are pretty much the same. Polity is congregational, with any associations above the congregation level usually limited to para-church evangelism organizations, orphanages, and nursing homes. Yet even within those two churches, there are congregations that can be classified as being more ecumenical and more sectarian.
The Christian Church (Disciples of Christ) split from the Christian Churches completely in the late 1960’s and while still part of the Restoration tradition, are generally more liberal in matters of ecumenism, Biblical criticism (especially allowing women to serve as pastors) and social justice, aligning with much of mainline US Protestantism. Baptism by immersion for salvation is still observed, yet the DoC today observes open communion, with all who proclaim Christ as Lord being welcome to partake while the CoC and Christian Churches generally observe closed communion, available only to those who have been baptized as an adult for the remission of sins. Many DoC congregations observe the western liturgical calendar, while the other two generally do not. Polity is still congregational, ultimately, but the DoC does have national and regional organization and assemblies. DoC churches predominate in the North and urban areas, while the CoC/CC’s are generally Southern and rural.
One very interesting difference in all three churches from the beginning of the restoration is in the view of millennialism with most people in all three churches generally being Amillennial or Post-millennial.
I grew up in the Church of Christ, and wound up as a member of the Disciples of Christ, primarily out of a reaction against the extremely conservative attitudes concerning women and divorce. It’s also not uncommon to find KJV-only adherents in the CoC and Christian Churches today. Doctrine in the CoC and CC’s today is generally ECT, with some acceptance of Annihilationist thought, though some of the more ecumenical congregations have some tolerance for a UR view. I’m completely comfortable in my DoC congregation, as there aren’t the attitudes towards divorced people re-marrying, and the very open-mindedness of discussion regarding many theological concepts. Our lady’s book study group read, and very much enjoyed,* Love Wins* when it first came out, and our pastors ( a husband/wife team) are both supportive of my view of UR, so I don’t have to try and hide that opinion as I would have in my old churches.
That’s about all I have off the top of my head right now. I’ll try to answer any other questions you might have. Richard Beck has some articles on growing up in a CoC in urban PA, which varied from somewhat to very different from my upbringing in suburban/rural congregation in SouthEast Texas.
Edit to add: In response to Jason’s point about the exclusivity of salvation in the CoC, they believe that only Christians will be saved, and that they are the true Christian Church and Body of Christ, at least in the more conservative side. They won’t generally admit that ideologically they function as a denomination, and denominationalism is still widely preached against.