门徒 is more formal and literary than 学生 (xuéshēng, student) or 徒弟 (túdì, apprentice). It implies deep devotion to a teacher, master, or religious figure. Common in religious and philosophical contexts.
history
门 (gate/door) refers to a school or lineage — a 门徒 is someone who has 'entered the gate' of a master's teaching. This reflects the traditional Chinese concept of 师门 (shīmén, a master's school/lineage).
