The Churches of Christ discussed in this article are not part of the ; The Church of Jesus Christ of Latter-day Saints or any other denomination within the Latter Day Saint movement nor have they ever been.
I make this distinction primarily for one individual because his mother once asked me if the church of Christ was a Mormon church.  I was absolutely shocked and tried to express to her in the strongest of terms that we WERE NOT nor had we ever been.  In retrospect, I'm not at all sure what this woman believed.  She certainly seemed not to be well-educated on a number of simple issues.
Churches of Christ are a movement of autonomous Christian congregations associated with one another through common beliefs and practices. They seek to model their congregations as closely as possible to their understanding on how early New Testament Churches operated.
Historically, Churches of Christ in the United states were recognized as a distinct movement by the U.S. Religious census of 1906. Prior to that they had been reported in the religious census as part of the Movement that had its roots in the Second Great Awakening under the leadership of Thomas and Alexander Campbell, Walter Scott, and Barton W. Stone.
Those leaders had declared their independence from their Presbyterian roots, seeking a fresh start to restore the New Testament church, abandoning man made creeds and interpretations.
Instead, they took the Bible's story of the early churches founded by the Apostles as their model.  The churches of Christ are non-denominational, welcoming anyone who wants to study just the Bible and nothing else.  Churches of Christ have no hierarchy beyond each local congreation.  As set forth in the Bible, each congregation has a minister and a group of elders.    
The names Church of Christ was adopted by the movement because they believed that this term  was found in the Bible.
Other names the movement did not believe to be biblical were rejected, such as Campbellite, Stoneite, Campbell-Stone movement, and even Restoration Movement.  
Modern Churches of Christ in America, and some elsewhere, are linked to the Restoration Movement, which was a converging of several Christians across denominational lines who sought a return to original, "pre-denominational" Christianity. Like many other individuals and Christian groups throughout the history of Christianity, the Restoration Movement was an attempt to seek doctrine and practice found in the Bible only rather than recognizing the decisions of councils and denominational hierarchies that had evolved since the first century.(That would include the Mormons who added to the Bible with the Book of Mormon).
In keeping with their history, Churches of Christ claim the New Testament as their sole rule of faith and practice in deciding matters of doctrine and ecclesiastical structure. Although they view the Old Testament as divinely inspired and historically accurate, they do not see its laws as binding under the New Covenant in Christ (unless they are repeated in the New Testament).
They believe that the New Testament demonstrates how a person may become a Christian, thus a part of the universal church of Christ, and how a church should be collectively organized and carry out its scriptural purposes.

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Self-identification
Churches of Christ believe that since the church was founded by Jesus, as recorded in the New Testament, the modern church and its doctrines must rely only on the New Testament for its doctrine and polity and thus transcend any other entities, traditions, movements, structures, councils, etc. that developed later within Christendom.
Members do not typically consider themselves to be members of a denomination, but prefer to simply be known as "Christians" They believe that Christians corporately should be referred to as the Church of Christ.Churches of Christ generally share these traits:

• They refuse to hold to any formalized creeds or statements of faith, preferring instead a reliance on the Bible alone for doctrine and practice. Each congregation is an


• autonomous, congregational church organization without denominational oversight


• Local governance by a plurality of male elders


• Baptism by immersion only performed on consenting individuals (i.e., not infants) in the name of Jesus Christ for the forgiveness of sins


• The weekly observance of Communion, also referred to as the Lord's Supper


• The practice of a cappella singing in worship (although some related congregations, known as Christian Churches, use instruments in worship)

 
Churches of Christ believe that humans (of accountable age) are lost in sin (but not born sinful cf Ez 18:4-22, Matthew 19:14)(Romans 3:23) and can be redeemed because Jesus Christ, the Son of God, offered Himself as the atoning sacrifice (Romans 6:23).
A main difference between Churches of Christ and other Christian churches is their doctrine of salvation. Churches of Christ believe that salvation begins when one obeys God's commands.
Here are the steps to salvation according to the Church of Christ; paraphrased:
1. One must be properly taught, and hear (Rm 10:17, Matt. 7:24),
2. One must believe-and build faith(Heb 11:16, Mk 16:15-16),
3. One must repent, which means turning from one's former life style and choosing God's ways (Acts 2:38, 17:30, Luke 13:3),
4. One must confess (Matthew 10:32-33, Acts 8:36-37),
5. One must be baptized (Acts 2:38, IPet 3:20-21, Romans 6:3-5) Also Mark 16:16, John 3:3-5, Acts 2:38, Acts 22:16, and Rev 22:14.
6. One must remain faithful unto death (Rev. 2:10)
This doctrine stands in contrast to some other Christian denominations, who place salvation at the moment of "acceptance of Christ," reciting a "sinner's prayer", or "asking Jesus into one's heart."
Baptism in churches of Christ is performed only by bodily immersion because in the New Testament the Greek term baptizo is always translated as "to immerse." Only those mentally capable of belief and repentance are baptized (i.e., infant baptism is not practiced because there is no example of such).