The “Other USC” should be the one in Los Angeles, the real USC is coached by Steve Spurrier.
If you mention, USC in any part of the country other than the deep south, 9 out of 10 people will assume you are talking about the Trojans and not the Gamecocks. This is probably proper, as well, since on almost any measurable academic or athletic standard, University of Southern California > University of South Carolina and usually by a wide margin.