Gypsum board is a considerably more specific, less generic, term than partition. My wooden house has some internal non-structural walls but none of them use gypsum boards (called plasterboard in British English).
Neither are they skimmed with plaster. They are instead faced with a very dense and flat hardboard.
Gypsum board is the term for a type of wall covering, which itself is part of a partition.
A partition is an interior wall assembly typically consisting of framing, (optional) insulation, and a wall covering (like gypsum board, but this could be anything: wood, shiplap, masonry, lath and plaster, etc.)
There are multiple levels of drywall finishing. A level 5 (highest grade) finish involves skim coating the entire gypsum wallboard with joint compound.
It’s not very common, but it is used in some commercial settings.
Neither are they skimmed with plaster. They are instead faced with a very dense and flat hardboard.