All we know for sure about the Hunter was that this was one of the 'shadows and evil spirits' that Melkor sent out against the newly awakened Elves (Quenta Silmarillion 3, Of the Coming of the Elves and the Captivity of Melkor). This is far from definite, but it implies that the Hunter may have been a minor Maia, or a lesser being of the same general order.

While it is never specified that the Hunter and the Rider were the same being, their few known attributes are identical, and on balance it seems reasonable to take them as different names for the same shadowy being. However, we do know that there were numerous dark creatures sent by Melkor to ensnare the Elves at this time, so it is by no means impossible that the Hunter and the Rider were separate entities. Indeed, it is even conceivable that the Hunter did not exist as a separate entity at all, since our only reference to him comes from an account of legends among the Elves.