"Horn" is the generic name for for both the hoofs and horns of animals. In Dwarf Fortress, hoofs and horns are functionally identical once stripped from their previous owners. Both are obtained by butchering certain animals, although horns are often only present on the male members of a particular species.
Creatures with horns and hooves can be very formidable in combat, especially since most of them are several times larger then your average dwarf. They have the ability to cave skulls or bruise internal organs. It is best to approach all hoof/horn wielding creatures with caution.