The Church of Christ churches are stand-alone individual congregations who find direction from the Bible for all beliefs.
Each congregation is directed by the leadership of the elders - men chosen to make the decisions of the church, hire the ministers, handle the direction and beliefs of the church. They are chosen based on the Bible instructions of what kind of men these should be......having only one wife, having raised their own children to be Christians, being soundly based on the Bible teachings. If any in the congregation can show reason a man is not so qualified, they can speak to the existing elders with their doubts.
They believe salvation is from Jesus Christ who died for the sins of man, they follow the direction of "repent and be baptised for the remission of sins and you will receive eternal life". They are Christians no doubt because they are following the same instructions given to the first century Christians.
They are not a cult, not the International Church of Christ (which is indeed a cult) and not part of a United Church of Christ group - as I have been a member all my life and have not become familiar with the United Church of Christ.
They are the Church of Christ and are really non-denominational although society tends to group people into denominations according to their beliefs. But, we get our beliefs from the directions given to the first century christians - not a man evolved creed.
Now, there are many different levels of Churches of Christ. Very conservative, more progressive, more progressive and liberal. But each is a stand-alone church under the direction of the designated elders. The young often want change, want instrumental music, want this - want that which over time causes varying degrees of conservatism, traditionalism, etc.
This link at UCC.org provides a history of the United Church of Christ and their origins. BTW, I am a Christian, but not of any of the Churches you mentioned. I am a Catholic. I am also an amateur genealogist, and have always had an interest in American and European history, including religion which has been prominent for good or ill in both places.