paddle driven cars may not be an automatic transmission in the classic sense. Nor is it a manual transmission in the classic sense. Maybe clutchless is a better term
I assume you're talking about the paddle-shifted transmissions found Ferraris, Lamborghinis, BMWs etc. in the recent past. These in fact are the opposite of 'clutchless'. They were basically manual transmissions electronically controlled and with the clutch and shifting actuated by hydraulics.
Nowadays they use some variety of dual-clutch transmission.