In general, they're different roles, but there's nothing to prevent one person from filling multiple roles, especially at a smaller institution. The answer probably depends upon the school or institution in question and whether positions are combined into one job.
I think "principal/headmaster" is more common. A director is a member of a school board which oversees the school management, but is not involved in the day-to-day running of a school as a principal/headmaster does.
I think "principal/headmaster" is more common. A director is a member of a school board which oversees the school management, but is not involved in the day-to-day running of a school as a principal/headmaster is.
I think "principal" is American English, and "headmaster" is British English. Also, a director is likely to be the head of a particular department, for example, a music director.