While sometimes we may hear people make a distinction between a "believer," a "disciple," or a "Christian," the truth is the New Testament uses these terms for the same people. In fact, often Christians are called "saints."
Each of these names simply describes a different aspect of being a follower of Christ.
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Disciple means follower and learner. It's used hundreds of times used in the gospels, 30 times in Acts, but not in any of the epsitles (letters to churches) or Revelation.
Believer is used 12 times (NASB) and only in Acts or the epistles and is a general term for all who have put their faith in Christ.
Christian is used three times. Luke notes that the first time the disciples were called "Christians" was in the city of Antioch (Acts 11:26). It was not a name the believers gave themselves and probably was intended as a put down or nickname. But in time it became the most common term for a believer.
Saint (hagios) is used 61 times in the New Testament (NASB). All believers are saints! It means one "set apart for," or sanctified (made holy), by Christ through faith. It's not a special class of people. So congratulation on your sainthood! See Acts 20:32; 1 Corinthians 1:2 for example).