While all cone snails are carnivores, or meat-eaters, different species of cone snails eat different types of prey. Some cone snails eat worms, others eat fish, and others eat other snails. As such, they are called vermivorous, piscivorous, and molluscivorous.
Cone snails have evolved to be very selective in their prey, and very particular about their environment. For example, some vermivores will only eat a specific species of worm, though they may have access to other types. In the laboratory, we have a hard time keeping cone snails alive since we are limited as to the fish we can feed our piscivores.
The links below will teach you more about each hunter.