No, I completely understand. But it's a lot easier to say "flatbread pizza" than it is to say "a flatbread with cheese and other toppings on it then baked in the oven". And here in the US you would be appalled at the number of restaurants that serve flatbread pizza. That's what it is called on their menus. It may not be proper but they do it.
And you will likely never have to suffer eating Papa John's. If you come to the US you should never eat at any of our pizza chains. Just go over to
TastyReuben's and let him bake you one, I'm sure it will be much better. I had some pretty great pizza at some sidewalk ristorantes when visiting NYC in the past. Nothing like that where I live, unfortunately.