None of the above.
Superior and subordinate is subjective and not relatable to this context, because a professor can learn from a teacher and backwards without the need of being superior.
Professional - client is also wrong, even though there was a college situations or a private school, the student is not the client, the client would be the people who is paying for the school, it can be the fathers or the tutor of the student, but no the student itself.
Employee - public: is subjective and not relatable to this context, students as itself does not belong as a part of a public, because they belong to an institution.