Wiki article says they can be visible ghosts or animated corpses. Because this debate also got me lost in wiki articles, it seems the primary difference between a large variety of monsters is their behavior and their origin.
Zombies generally refer to largely mindless, anonymous creatures--in most pop culture, zombies don't have personal connections to their targets.
Revenants, on the other hand, seem to rise specifically to target those who they were close with in life (though that's a later addition to the folklore).
Draugr (Norse for "ghost) are, ironically, animated corpses. But the concept is that they guard their own graves from robbers, as Norse burial send them into the afterlife with a great deal of wealth. Draugr would, on occasion, leave their crypts at night to attack the living (almost always leading to horrific killings), but it seems this was usually out of revenge or jealousy. But it doesn't necessarily say this is personal, like with the Revenant, but rather suggests that all Draugr end up loathing the living. They share the feature of an insatiable appetite (perhaps a symbol of their desire for life) with modern zombies.
There are WAY more, of course. Because many, many (if not most, or even all) cultures have legends of the dead returning. I just chose these because they are the ones I see most frequently in media.