Upvote:4
Congregationalist churches are of the Protestant Reformed tradition, and go way back to the English Civil War when the King tried to gain control over the governance of the Church. Back in the mid 1600’s, Puritans resisted the influence of the Church of England and broke away. By the early 1800’s, the Congregational Church had established itself in America with its own form of governance, with a strong emphasis on the autonomy of the local church, and tolerance of doctrinal variations. In 1957, the Evangelical Reformed Church merged with the Congregational Christian Churches to become the United Church of Christ. The Conservative Congregational Christian Conference was formed in 1948 in opposition to the liberal theology making inroads in other Congregational churches. Then, in 1955, the National Association of Congregational Christian Churches was formed.
More information on the history of Congregationalism here: https://www.gotquestions.org/congregationalism.html
The Churches of Christ came out of the Restoration Movement:
The Restoration Movement began in the early 19th century... Among the most influential leaders of this movement were Alexander Campbell and Barton W. Stone. Although the fundamental views remained, in 1906 this group split. The followers of Campbell and Stone divided into two sects, called the Church of Christ (Non-Instrumental) and the Christian Church (Disciples of Christ). Over time many additional schisms have formed from these core groups as well. Currently there are three major and several minor groups who trace their roots back to the Stone-Campbell Restoration Movement: the Christian Churches/Disciples of Christ, Churches of Christ, Independent Christian Churches, Churches of Christ in Australia, Associated Churches of Christ (New Zealand), United Reformed Church (UK), and others... Although a key principle of the Restoration Movement is concern for Christian unity, the history of the movement is itself riddled with numerous splits, re-splits and schisms. Source: https://www.gotquestions.org/Restoration-movement.html
Perhaps the most significant difference between the beliefs of Congregationalists and the Churches of Christ is the view of the latter that baptism by full water immersion (for consenting adults only) is a requirement for salvation. Equally worrying is the view that a person must continue to strive to maintain their salvation by doing works. Insisting that the use of music in worship is unbiblical almost certainly won’t affect anybody’s salvation, but it should be of concern that any religious group would be so dogmatic. Even the Free Church of Scotland has now conceded on that one! The article in the link below came to this conclusion:
Many Church of Christ churches are in fact solid, biblically based churches. There are many Church of Christ churches which declare the true Gospel of salvation by faith alone, through grace alone, in Christ alone. At the same time, with an extreme over-emphasis on the absence of musical instruments, with a claim of exclusive access to salvation, and with a doctrine of salvation that is borderline (at best) works-based, there are other Church of Christ churches that should definitely not be attended / participated in. This requires discernment on the part of a believer considering joining a Church of Christ church. The answer to the question depends entirely on which type of Church of Christ church it is. Source: https://www.gotquestions.org/Church-of-Christ.html
I hope this information will help you in your research into the differences and connections between the two groups.