> In Italy there's a bunch of things called "pizza" which are not round flat bread.

True, although the canonical/widespread pizza is the round/flat one.

I've never heard of "Pizza di Pasqua" and "Pizza sbattuta" in Italy (I don't doubt they exist, but they must be very uncommon).

Pizza in teglia is common, at least in certain parts of Italy; I believe it's generally sold in bakeries rather than in pizzerias (restaurants).

Pizza alla pala is not so common in Italy, at least in restaurants (not that I remember). In other countries is very common in takeaways.

There's also a type of pizza that is round but thick, and with lower-quality toppings. I can't find any reference to it; it's somewhat widespread over Italy, but considered a "lesser pizza" :)