I believe the term you're looking for is called Subquery which is what is in your WHERE clause in your second example but can be in the FROM clause too. Also to give a Subquery a specific name so you can reference it, you would use a Table Alias.

I just read your examples closer and understand your question better now. Your second example that you were doing uses a subquery but the first example your professor was doing is called an implicit inner join. It's just a shorthand way to write FROM employee EMP INNER JOIN employee SUP ON SUP.employee_ID = EMP.supervisor_ID like @stickybit commented.