Not at all, they are probably talking about horrible Dayton Style pizza. For when you want pizza but it needs to be thin, unsatisfying, greasy, and difficult to eat.
People who eat Dayton-style pizza are like the city of Dayton itself—smelly inside and bereft of true purpose. Those of us in the US who haven't been so psychically damaged wouldn't eat that shit.
(I'm only just learning about the disgusting gutter pizza. I don't like Dayton because my last company was slowly destroyed over several years by a company that was headquartered in Dayton. I associate the city with the asshole who was CEO. Fuck you, Chris! I've heard Dayton is, at worst, not great, so take my comment as the joke it is.)
Hard to believe but they do. Note the blackened edges to make it even worse. It isn't a nice char like you get with Neapolitan, or even the seared cheese you get with a good Detroit or Pan, it's just burnt.
There are many American pizzas that are great, Chicago deep dish, NY, Detroit, on and on, Dayton style is not one of them.
Tomato soup in a bread bowl, with cheese. Not quiche, the filling isn't egg-based.
It's delicious. And since the Italians call just about any round bread with toppings pizza (e.g. Bartolomeo Scappi's pizza was cake with powdered sugar & saffron toppings) it's pizza. As is New England clam chowder in a bread bowl!
The only correct way to cut (not too gigantic) round pizza is into six parts so you get equilateral triangles (well, modulo a curved section) which is ideal for holding.
Home-made pizza rarely if ever is round, though, in which you probably don't want to go for squares but eyeball some appropriately-sized rectangles.