If Pizza Hut is your reference point, they periodically try their hand at the various alternate styles.
The Edge is their tavern cut
The Sicilian is their Detroit style
and the Big New Yorker is obviously their NY style.
These aren't permanent menu items, but limited edition offers that they roll out from time to time.
and if all three styles have pepperoni as the single topping, they're very similar.
also, throw in their Pan pizza from back in the 80s - perhaps they still have it
rust is just that way of delivery regardless of shape IMO, The Old Chicago chain here has good (not great) pizza. They offer 4 crusts - OC Thick, Ale Crust, Tavern Thin, & cauliflower
Great pizza to me is more about the taste of sauce, the freshness & quality of the toppings, & taste of the crust. Then if everything is in good balance and is cooked to the correct doneness. (balance refers to not too much crust, not too much sauce, not too few toppings or too many.)
the shape of the crust and the thickness of the crust doesn't mean much to me. I usually pick a thinner crust because I try to limit my carbs. But, I've not tried cauliflower.