I think the advertising phrase "End to end AI" gave the impression the cars were learning on their own.
I think the phrase was "end to end neural networks" which replaced 300,000 lines of hand written software code. As you say, the NN training happens in huge data processing centers and is downloaded to the cars in the periodic software updates. The cars do not update the NN themselves.
There is, however, feedback from the cars to Tesla's data centers, and this is used both in NN training and map updates. So the cars are leaning from their experiences, but only in a collective sense.
As discussed earlier in this TMC thread, some map data is downloaded to the car while driving as part of the navigation process, to a car's behavior can change from one day to the next without a full software update. But this does not imply the car learned anything by itself.
Also as I have said before, I hope Tesla does eventually let the cars learn. For example, mine has some favorite potholes it always bumps through, so I have to disengage AP for a couple seconds to manually steer around them. This happens every day till the city comes out and patches the road. The car could learn, like we do, from the first hard bounce.