The automatic transmission used in F1 cars is not at all comparable to the automatic transmission in consumer cars.
While the automatic transmission in F1 cars allows for fine grained control of the individual gears and just automates the gear-switching, consumer cars typically control which particular gear should be used at any moment of driving, and this difference is clearly noticable while operating the vehicle.
The sports automatic we're talking about here goes into manual mode if you use the paddles on the steering wheel. And then it operates the same as an F1 car, you are in manual control of the gears and the "automatic" side of it only steps in when the engine would otherwise stall (F1 calls it anti-stall and does it in a different way, but the effect for the user is the same).
Other than that of course an F1 gearbox is a very different and much more advanced piece of technology. I was talking about the way the user operates it, that's equal for a road car with paddles.
There is also two types, torque converter based one ("classical" auto) and DSG which are closer to "automated manual", the good ones have lightning quick shifts and are overall performance-wise better than automatics on every front. Well the good, ones, bad DSGs also happened.
While the automatic transmission in F1 cars allows for fine grained control of the individual gears and just automates the gear-switching, consumer cars typically control which particular gear should be used at any moment of driving, and this difference is clearly noticable while operating the vehicle.