As far as I know Pro/Am is Teacher/Student competition. I have never heard of teacher/student events at a competition (as something separate). The student alone is judged. Pro/am is never same sex (at least not that I have seen in North America). As a female pro you can only dance with male students. If you get paid to teach dancing then you are a pro. You can compete as a pro with another pro or you can do pro/am and dance with your student. You can't compete as an amateur.