This isn't nuance - none of it is relevant. Q in the movies (the only place he originally appeared) is obviously based on a CQMS someone knew and the Q branch

This isn't nuance - none of it is relevant. Q in the movies (the only place he originally appeared) is obviously based on a CQMS someone knew and the Q branch in the books is almost certainly based on the abbreviation Q for the word Quartermaster in the Quartermaster's Stores.