The word “Christian” comes from the Greek word “CHRISTIANOS,” and it means “follower of Christ” (Strong’s Concordance). It is only used three times in the New Testament (here, Acts 26:28, and 1 Peter 4:16). This name did not originate with the followers of Christ but was a term of scorn used by the opponents of Christianity to criticize the followers of Jesus as acting just like that Jesus of Nazareth who claimed to be the Christ.
Although the unbelievers did not intend this name to be flattering, it was actually one of the highest compliments that a believer could be paid. The church adopted this name for themselves and used it to describe themselves as early as the second century A.D.
Disciple - mathētēs - a learner, pupil. The term applied to students of a Rabbi. (Teacher). The ‘disciples’ were not strictly ‘Christian’s’. To become a ‘Christian’ you need a revelation of who Jesus is. And for their initial period of time with Jesus they didn’t have this …
MAT 16:13 When Jesus came into the region of Caesarea Philippi, He asked His disciples, saying, “Who do men say that I, the Son of Man, am?”
The initial answers reflected those of disciples, not christian. However Peters answer reflected that he was - and Jesus said that Peter only knew that because it was revealed to him.