The term “Christian” is found only three times in the New Testament and always in the mouths of the critics, not the believers themselves. Within the New Testament, the believers never used that term of themselves. The terms “Christian” and “Messianic” really mean the same thing, but the former is from a Greek source and the latter from a Hebrew source. The Greek, Christianos (Christian), is equivalent to the Hebrew, Meshichi (Messianic).
Today, the term “Christian” carries a lot of negative baggage for Jewish people because of what has been done to them throughout history in the name of “Christ,” and so the Jewish believers prefer to call themselves Messianics rather than Christians. The most common New Testament term for believers was “saints,” but because that now carries a lot of Catholic baggage, most believers do not refer to themselves that way.