Here's how it works.
A majority of paddle shift cars have a manual transmission with a robotic clutch, so there is no clutch pedal. (Toyota MR2 Spyder, Lamborghini Murcielago and Gallardo, Ferrari Enzo and 360 Moderna, Formula 1 cars, etc.)
There are some cars, like the Pontiac Grand Prix Comp-G where it's an electronically shifted automatic, not a robotic clutch manual. All GM automatic transmissions with a -E after the designation are electronic and can be customized for this feature (4T65-E, 4T60-E, 4T40-E, etc.). All cars that have the "Slap-shift" manu-matic feature, like the Acura TL and RL, are electronic automatics, but could be configured to have paddles or shift buttons on the wheel.