They are made of clay. But clay pigeons come is different varities of structure, look, and size. Also they are used for different kinds of shots for example... a bateu, or seandell, or rabbit, as well as quartering, crossers, outgoers...
Clays are called exactly that - clays. Sometimes they will be referred to as targets or clay pidgeons, but I am not aware of any other commonly used terms for clays.