There are so many different kinds of pizza and all of them are amazing. The combination of tomato sauce, cheese, bread, and toppings is just genius. Its aroma can be irresistible. Though when done badly, the crust can be hard, the cheese rubbery and the whole thing just unappetizing. But when done right, it is amazing.
The thin crust pizza derives its uniqueness from its thin crust, as people can see from its name. In order to be really delicious, that crust needs to be crispy, as if it was a toasted piece of bread. And like a toasted piece of bread, if the crust is burned, it can completely ruin the taste and the pizza experience. But a little char is not so bad, it gives it a smoky flavor. The toppings put on the thin crust variety can range from anchovies to artichoke. Pretty much anything goes as more and more people invent different kinds of specialty varieties, like Hawaiian, Margarita, or Hamburger. Most places will also allow customers to make up their own specialties by paying per topping.
Coming from that style is the New York-style pizza. This type cropped up in the early 1900's. It goes a little beyond just thin crust. It is known for being very large, thin and wide. More than that, it is known for being folded in half in order to eat. Folding it and eating it came from the necessity of wanting to eat it on the street, and the fact that the piece is so big makes it very hard to eat it flat. So people fold it, hot dog style, meaning lengthwise instead of widthwise.
Another variety that is polar opposite from the thin crust or New York-style is the Chicago-style pizza, which is known for its very thick crust. It is so thick because it is baked in a deep pan with high sides. The crust is incredibly thick and there is so much cheese that usually just one slice is enough to fill up most people. And in general, the deep-dishes are more expensive than their thin crust cousins. This kind is often eaten with a knife and fork because it is so big and has such a thick crust. This style came into being around 1943.