College or high school?

Weezie mentions the graduate ceremony as their "baccalaureate," which would imply that this was a college, no? I've read some people refer to the school in the film as a high school, which seems valid given the level of power the headmistress has over the girls— but could it not just be a strict private college? It's never explicitly stated, but my assumption was that this was set at a college, not a high school as some people have said. Am I wrong?