Yes, coffee is categorized.

There are two main types of coffee bean: arabica and robusta. Most ground coffee that you see at the store are a mix of both. Usually 70% arabica and 30% robusta. Arabica is known more as the "better tasting" coffee while robusta has about 50% more caffeine and is more pricey. 

Arabica has a few different branches of beans as well. The most commonly known beans are Colombian, Jamaican Blue Mountain, and Sulawesi. Robusta beans don't have a large variety of different beans. The most common is the Civet and an expensive Kopi Luwak. The beans aren't necessarily definable from any other bean, but you won't know the difference until you've tried them!