Student derives from 14c French so it might be translated as a student but it didn't mean or have the root meaning of student. A man can be a student and fail to learn anything. The ability to pay tuition fees can make a man a student.
The word disciple conveys a definite meaning.
There were the twelve. Disciples, apostles. There was a different number of disciples. Or just a student or follower of Jesus. As we too can be without Jesus physically being present to teach.