There are multiple alien races.
The "primary" aliens at the heart of the conspiracy arc are the greys, which include the colonists (but not all seem intent on colonizing Earth) and, apparently, the long-clawed aliens (a different stage of their life cycle).
The faceless aliens/bounty hunters may or may not be the same race as the greys; at the very least the latter certainly work closely with them (at least the ones we've seen), although the former oppose the colonists. Their shape-shifting tendencies make it hard to be sure what race they truly belong to, though.
The purity -- aka "black oil" or "black cancer" -- is apparently an intelligent virus. However, given that infection by purity can result in the host being impregnated with a long-clawed alien (which in turn sheds its skin later to become a grey), this may be just another stage of the natural life cycle of the greys, rather than a distinct alien species.
So those are the ones involved in the main conspiracy story arc throughout the series -- anywhere from 1 to 4 distinct species of extra-terrestrials.
The "monster of the week" episodes, however, have given us several others, including the Kindred, the gaseous Martians, a spider-like creature, and more -- including multiple MotW episodes where the nature of the creature in question is never quite answered, and it may be an alien -- or it may not be (for example, the ice worm parasite, which Mulder theorized to have come to Earth on a meteorite, but that was never confirmed nor refuted).
So, yes, Earth is being visited by multiple races from at least (and most likely many more than) 2 different planets.