Hello 미희, your right! 대학원생 or 석사 과정 학생 means master's student and 박사 과정 학생 is for a doctoral student :)

대학원생 means any "graduate student" because 대학원 means graduate school, and 생 means a student.

제 친구도 박사과정중인데, 그냥 자기소개할 때 대학원생 이라고 하기도 해요. 대학원생(Rough meaning) includes 석사과정, 박사과정. but most of people think 대학원생 is close to student who is in master's course. *Both is OK. But People who in their doctor's course may like to say '박사 과정 중입니다'