Poseidon vs Neptune

Is Neptune the same as Poseidon? In myth, yes — Ovid's Neptune floods the earth with the trident and Virgil's Neptune calms the storm as the brother who won the sea by lot. In cult, no — Livy's Romans hold games for "Equestrian Neptune", the Consualia, at which the Sabine women are seized; no Greek text ties Poseidon to that.