The traditional RPG definition is neither - the Greyhawk Campaign or the Blackmoor Campaign is a setting in which many individual adventures take place, with a linked and interacting series of PCs. It's not a series of adventures undertaken by a particular group, but neither is it the entirety of the world in which the particular campaign takes place. It's the Greyhawk Campaign, not the Oerth campaign.
Yeah, well a military campaign is usually even more limited in scope than a series of adventures with the same characters so I'm not sure I'd base the definition of campaign, with respect to RPGs, on military definitions.
I'd define a campaign as the continuity of gameplay provided by the DM.
Does game system matter? If I run D&D, GURPS, and M&M games, are they all part of the same campaign?
Does game system matter? If I run D&D, GURPS, and M&M games, are they all part of the same campaign?

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.