New York style pizza is thin crust, easy on the sauce and usually a crispy, flaky crust made out of a high gluten bread flour. It is round and mozzarella and tomato sauce are the main ingredients. The slices can be folded over and eaten.
Other types of pizzas use blended cheese - provolone, mozzarella and sometimes even Cheddar
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Sicilian pizzas are square with a thicker dough and are made in squares.
The Chicago style deep dish is thicker dough with layers and layers of ingredients plied high. It can have a dough covering like a pie or sometimes not.
I think Frisco Frankie knows deep dish as having a dough topping and I am not used to that. when I visit him next, I am going to beg him to make a deep dish pizza for us!! (* hint: Hope you are reading FF - I will buy the ingredients!)
The 1st NY pizza place was Lombardi's which opened in 1905 in Manhattan.