Earlier quoted context omitted.
Often that means that the university claims rights in the IP produced, certainly [way back] when I matriculated it was required of all students to sign a waiver giving rights to the Uni for any works created whilst being a student. The first I heard about it was at the matriculation table when I'd already gone up. Perhaps this sort of thing doesn't happen elsewhere or as been deemed inappropriate.
This is only true for graduate programs where the school is paying for your tuition via a research or teaching assistanceship. For undergraduates, who traditionally pay for their own tuition, or for graduate students under scholarship, they own all of their own work.
This depends on what the work's being done for. If it's for a class or a credit giving research project, the university usually does own the IP in most cases.
However, if it's a side project that's not using any of the university's resources, the university shouldn't have any rights to it.