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.
I’m from Louisiana and USC to me was always the Gamecocks.
Coach Steve Superior is now 58-35-0 at SC, 7 wins away from being the coach with the most wins in their history. He's also 3 losses away from being the coach with the 3rd most losses in their history, passing Lou Holtz who is 33-37-0. Rex Enright is 64-69-7 and has the most wins and loses. 2nd most loses goes to Paul Dietzel at 42-53-1.