In the Bible the Church of God and the Church of Christ are the same. There are various passages that refer to the Church for which Jesus died as one or the other, showing the two are interchangeable.
“To the church of God which is at Corinth” (1 Cor. 1:2)
“Now you are the body of Christ…” (1 Cor. 12:27)
“Give no offense, either to the Jews or Greeks or to the church of God” (1 Cor. 10:32)
“Or do you despise the church of God and shame those who have nothing” (1 Cor. 11:22)
“…how I persecuted the church of God beyond measure…” (Gal. 1:13)
“…which is the church of God, the pillar and ground of the truth” (1 Tim. 3:15)
“…on this rock I will build My church…” (Matt. 16:18, Jesus speaking to Peter)
“…and gave Him to be head over all things to the church, which is His body…” (Eph. 1:22, 23)
“…for the edifying of the body of Christ” (Eph. 4:12)
“The churches of Christ greet you” (Rom. 16:16)
Notice in Acts 20:28 that Paul states the “church of God which He purchased with His own blood.” This shows that (1) Christ is God and (2) the church belongs to Him because He bought it with His blood.
The question, though, is likely directed at what is found in modern times; a time filled with confusion over denominations of men.
The typical “Church of God” in your area is not the “Church of Christ” found in the Bible. Churches of God generally have different:
Churches of God and churches of Christ that are following the New Testament differ in the following ways:
- Instrumental music vs. acapella singing
- Entertainment, recreation, etc. vs. Spiritual focus and work authorized in NT
- One-man pastor leading the church vs. plurality of elders (cf. Phil. 1:1)
- Part of a denominational body vs. local, independent congregations