Pizza comes to the rest of the world from Naples, Italy.
Italian pizza (Neoplitan Pizza) - The group, Associazione vera pizza napoletana, created a standard pizza so the true traditional Neoplitan pizza is not lost to commercialization and "Americanization."
Also, pizza in Italy is different from region to region.
Neopolitan (Naples) has a thin crust pizza while pizza in Rome are rectangular with a thin crispy (cracker-like) crust and no cheese. More like a foccacia.
I agree with you that they like single toppings of meat, but they do use cheese and instead of a long cooked tomato sauce we use in the USA. Italian pizza uses a fresh tomato, garlic, oregano, olive oil puree.
As mentioned cheese is used, but it's sliced mozzarella, not shredded.
As to the rest of the pizzas, other countries have taken that idea and adapted to their own liking - Korean (Kimchee), Taiwanese (seafood) and American (everything piled high), which you correctly summarized.
I believe American Pizza to be an adaptation (not a fusion) of the original Neopolitan pizza.