There are usually two possibilities for this to happen. The first type: the enrollment ability of tutors, which is the most common phenomenon in the same school. Some teachers have places but can't recruit students, and some teachers have fewer places but more students apply. In this case, other teachers will borrow places. The second type: the requirements of the school are related to the requirements of the school. Some schools require associate professors to bring two students, professors to bring three students, and some schools even allow associate professors to bring five students by themselves, which is why you mentioned this situation.
Postgraduate is a kind of qualification certification of national education, which is generally carried out by ordinary universities with master's and doctoral degrees. You can also be called a graduate student after graduation, which means someone with a graduate degree.