only difference is that Chicago appropriated the name "pizza" when that word had previously been applied to a different food. Maybe it is analogous to the word "pepper." Crushed peppercorns produce a seasoning called "pepper" that had been used in the old world for a few thousand years. It is distinct from the chili pepper that had its origin in the Americas. Nevertheless, Americans call chilis "pepper" because it was thought to be spicy like pepper. It is not pepper. It is a chili.
Arguably, New York appropriated it from the Italians first.