Full-grain leather is the tanned hide of an animal with the hair removed, according to About.com. Full-grain leather shows the grain of the leather and is considered the top grade of leather.
Top-grain leather is not the same thing as full-grain leather. Top grain refers to leather that has had an artificial grain applied to it. It is a lower quality leather than full grain.
Leather is also categorized by the animal from which it is made. Lambskin is from lambs, kidskin from goats, calfskin from calves, pigskin from pigs and cowhide from cows. Suede is leather with a buffed flesh side for a softer texture.