If you go back into the history of the NY style, you will see that the basic NY style pizza was made using flour, water, fresh yeast and salt. The flour originally was all-purpose flour but over time pizza operators used bread flour and high-gluten flour as they became available and popular for that style. The bread flour and high-gluten flour were commonly bleached and bromated. Sometimes they were just called "pizza flour". There was no sugar or oil used in the dough, and the dough was mixed by hand (before Mr. Hobart invented the commercial mixer) and fermented at room temperature (commercial refrigeration had not yet been invented). Dry yeast products such as ADY and IDY had not yet been invented (IDY was invented just after World War II and IDY was invented in the 1970s), so the yeast used was fresh yeast. The pizzas were typically baked in high-temperature coal fired ovens. When deck ovens were invented and became commercially available, oil and sugar started to be added to the dough. When refrigeration became commercially viable for cold fermenting dough, it allowed pizza operators to make dough and be able to use it for more than one day. The end product pizzas were typically quite large, with 18" being typical. In some cases, they were even larger than 18".
Today, if you were to investigate what NY style pizza operators are doing, you would find that all of the above measures are being used by someone somewhere. However, over time, there has been a movement toward the use of high-gluten flours and the regular use of oil in the dough. The flour is most likely to be bleached and bromated. Sugar might also be added to the dough, especially if the dough is to be cold fermented for more than a few days. And dry yeast products are regularly used. Most of the NY style pizzas today are likely to be baked in deck ovens, although there are still coal-fired ovens being used to make the earlier NY style pizza, often called the "elite" style to differentiate those pizzas from the "NY street" style. The elite style pizzas come in the larger sizes although the NY street style pizzas can come in a wide range of sizes, including 12", 14", 16" and 18", with the most common size still being the 18" size. There is also a wide range of toppings for the NY street style and bake times also tend to be on the high side, much longer than would be used to make the Neapolitan style, which are typically baked in very high temperature wood-fired ovens with bake times of under about 2 minutes and often under a minute. Also, the Neapolitan style pizzas rarely get above 10"-12" in size. And, as John noted, the flour used for that style is usually an unbromated, unbleached, unmalted flour such as the 00 flour, there is no sugar or oil used in the dough, and the pizzas are sparsely topped. The sauce is typically made from Italian San Marzano tomatoes and the cheese can be fresh mozzarella cheese of buffalo mozzarella cheese. The NY style pizzas typically use canned domestic tomato products and processed mozzarella cheeses.