various institutions include schools , Federal governments , courts , etc.

These words can all apply to a university or parts thereof, although as other people point out, the words can also apply other places, too. In the context of a university, "institution" refers to the university itself. eg "Harvard is a fine institution." "Faculty" refers to the academic staff, the professors, lecturers, etc. "Faculty" could also refer to a large division within the university, eg "the Faculty of Law" might be the law school, or the "Faculty of Sciences" could include all of the science subjects. "Departments" refers to individual subjects like History and the associated buildings, faculty, classes, and students for that subject.

A government also comprises lots of department , for instance , military department or healthcare department.