I actually have to make an amendment, because pizza doesn't have to be cooked in a dish, I've actually even cooked pizza without a dish. I was thinking about it more (what makes pizza a pizza) and I would say that there are a few different criteria.

1. Oven baked. No one is eating raw bread dough, so there is no such thing as an uncooked pizza, and you can not develop a crust without an oven.

2. Dough. Pizza dough differs from bread dough traditionally in its ingredients. Where this part gets tricky is with some pizza having a non traditional dough either for convenience or to be different (sourdough is a somewhat common pizza base). So I would add in that the shaping of the dough is key. After proofing, the dough of a pizza is shaped into that tradition pizza base shape, which will remove most of the fluffiness of the dough, this is what really separates pizza from bread. Also there's a bunch of differences in the fermentation process of pizza dough that you wouldn't do with traditional bread.

3. Toppings. I've never seen a pizza without a topping, a pizza without a topping is a flatbread basically. I've seen them with minimal toppings (oil, seasoning and herbs) but at that point you're really pushing the boundaries of where flatbread stops and pizza begins (traditionally they're made with a slightly different dough, but not always). Flatbread becomes pizza when you add a sauce and/or cheese. While some flatbreads still feature cheese melted on top which makes defining them tricky, I would say if it's got cheese on it it's more pizza that flatbread.

That's the best and most simple way I would be able to describe what defines a pizza. Also, before anyone mentions it, dessert pizzas do not count in the same way a gummi pizza wouldn't count.