I'm sure you have cheese pizzas and they're distinct from quattro formaggi. I'm not saying there isn't. I'm just answering your question. As a non-american, the only pizza with cheese is quattro formaggi. All the others are just "pizza". Because all the others have tomato sauce + mozzarella as a base. Except supermarket pizzas which sometimes have cheaper cheeses on them. But they're still just pizza, not "cheese pizza".