Even so, in eve there are only small aspects that span servers simultaneously (the market place, and maybe other things too--I haven't played in a year or so).
The unique thing about eve is being able to jump between "realms" or servers or "shards." That gives the illusion of playing together in a much larger world.
I've never played WoW, so I don't know if you can jump between shards or realms, or if they are treated more like parallel dimensions.
As you suggested, it refers to multiple "parallel dimensions" between which the playerbase is split to avoid overpopulation; that's how almost all other MMOs work. Whether each of those runs on a single physical computer is irrelevant to anyone except the host.