Traditional pizzas don't always come with tomato sauce, but that is how most people think of them, since modern pizza is based upon recipes brought over by poor southern Italian immigrants. Most of those kinds of pizza were thin crust, with lots of tomato sauce; this is common with Sicilian style, which is quite heavy. Some Mediterranean pizzas use olive oil and garlic as a base; usually this is Greek style. I've also seen alfredo sauce pizza, but that is likely an American creation. Putting ketchup and mayo on pizza is disgusting, and I can't imagine why anyone would do that.