There were several men named Gaius

Ephesus (Acts 19:28-30)
"When they heard this, they were furious and began shouting: 'Great is Artemis of the Ephesians!' Soon the whole city was in an uproar. The people seized Gaius and Aristarchus, Paulís traveling companions from Macedonia, and all of them rushed into the theater together. Paul wanted to appear before the crowd, but the disciples would not let him.
Traveled with Paul (Acts 20:4)
"He was accompanied by Sopater son of Pyrrhus from Berea, Aristarchus and Secundus from Thessalonica, Gaius from Derbe, Timothy also, and Tychicus and Trophimus from the province of Asia."
Baptized by Paul (I Corinthians 1:14, 15)
"I thank God that I did not baptize any of you except Crispus and Gaius, so no one can say that you were baptized in my name."
It is uncertain which Gaius was the friend of John in this letter.
It could be another Gaius.

Look at the evidence and make your choice.

Acts 19: Gaius the courageous worker with Paul.

Acts 20: Gaius from Derbe.

I Cor. 1: Paul baptized Gaius.

3 John: John seems to include Gaius in his children of the faith.

It makes little difference, except in how we understand the 3 John text.