There's two, and sometimes three, basic differences
1: A traditional manual clutch is about the size of a dinner plate. With a DCT, one of the clutches looks like a much small plate, and the other clutch is a wide band/ring
2: The pressure plates are of a slightly different construction compared to a traditional manual
3: Situational: There's two types of DCT clutch systems - Dry clutch and Wet clutch. The 7-speed DCT in the GT is a Dry clutch type; the 8-speed found in the i30/Veloster N and a few others is a Wet clutch - the entire clutch/pressure plate assembly lives inside an oil bath, for better heat management