NY style is thin and flimsy always cut from a round (Cheese or Pepperoni). Grease will drip off it. You have to fold it in half lengthwise and use two hands to keep the cheese from sliding off it. After one or two bites it'll be stiff enough to eat one handed.
Chicago style is THICK and doughy from a deep dish pan. Real tomatoes, sausage, and cheese. Sometimes you have to eat it with a fork.
Deli style (my term), is either XL flat pan or round. thicker than NY style, and uses alot of different toppings. Here's where you get creative. The crust is thick enough to pile on the toppings but not deep dish.