In the Forward [sic] to Volume 1 of OD&D, Gary Gygax notes two things. First,
While it is possible to play a single game, unrelated to any other game events past or future, it is the campaign for which these rules are designed. (emphasis mine)Second, he comments on the "longevity" of the Blackmoor and Greyhawk campaigns. Taken together, it seems clear to me that an OD&D campaign is something that is 1. "Larger" than a single "game" (i.e. adventure) 2. Maintains continuity between individual adventures 3. Not tied to a single "story" or focused on the exploits of a single group of characters.
The third item is, I think, key. We know that, in the Greyhawk campaign at least, there were multiple groups of characters, some of whom did not interact with one another regularly, if at all. I am not certain if the same was true in Blackmoor, but I believe it was. I know that it was the case with the Tékumel campaign, with its Monday and Thursday Night Groups. In each case, though, we speak of a single campaign, not multiple ones. That is, we don't speak of the Greyhawk campaigns but instead the Greyhawk campaign, even though the actions of players not necessarily playing in the same groups or on the same nights (let alone the same adventures) had an impact on one another. A "campaign" is thus what might be called nowadays, in video games jargon, a "persistent world." Thus, a campaign could -- and often did -- outlast the lives of any particular PC or series of adventures. A campaign continued on, changing and growing as the years wore on and the actions of myriad characters affected it.
While I'm not certain this is the case, I get the impression that contemporary gamers don't think of a campaign in this way. For them, a campaign is a series of adventures involving the same group of characters (more or less) and that comes to an end when its story is finished. Whereas the older understanding of a campaign was geared more toward sandbox play, the newer one seems built around the notion of a story or at least a "theme." The popularity of the Adventure Path style of play in 3e (though it has antecedents going back to 1e, Dragonlance foremost among them) is, I think, good evidence of this shift in the understanding of a campaign. Listening to gamers speak nowadays, they talk of having played several campaigns, even if all these campaigns are set in the same persistent world. It's a subtle difference, to be sure, and not a universally pernicious one, but I think it's a shift nonetheless.
I'm still not sure what to make of this or even if my intuitions are correct. However, I can't shake the sense that campaigns are different now and viewed differently and that's had a profound impact on the way RPGs are designed and marketed.