They are two words for the same thing.
BEAK: early 13c., "bird's bill," from O.Fr. bec (Fr. bec)
BILL: "bird's beak," O.E., related to 'bill', a poetic word for "a kind of sword" (especially one with a hooked blade), from a common Germanic word for cutting or chopping weapons (cf. O.H.G. bihal, O.N. bilda "hatchet," O.S. bil "sword")