Peter Reinhart, in his cookbook American Pie, refers to the pizzas produced by places like Lombardi's, Totonno's, John's, Grimaldi's, DiFara's, Sally's and Pepe's as being "first generation Neo-Neapolitan" pizzas. Many of these use coal-fired ovens which are known for producing a lot of charring of the crust through carbonization. Reinhart puts the New York style of pizza, which he says is the foundation of the pizza-by-the slice business, in the "second generation Neo-Neapolitan" category. (The "third generation Neo-Neapolitan" category includes mainly the West Coast pizzas such as produced by Wofgang Puck, The California Pizza Kitchen, etc.) The pizzas I saw on the streets of NY were clearly within the second generation Neo-Neapolitan category.
The other thing I noticed about the NY "street" pizzas, which you educated me on some time ago, is that the rims of such pizzas are rather small. I happen to prefer a nice, large, chewy rim--it's one of my favorite parts of a slice of pizza--but apparently a large rim is not a standard characteristic of a NY street style pizza.