Now, imagine a game in which the players bring different characters in from time to time, mixing and matching adventuring parties for different adventures, and this keeps going on for years with the only constant being the setting. The timeline more or less advances throughout with the actions of earlier PCs being written into the history for later PCs to know about.
Bingo!
Also throw in the idea of players occasionally joining and leaving and you've got my definition of campaign pretty much bang on.
(long essay warning)
Let's take my last (self-defined) campaign as an example; and you tell me when it stops/starts/continues being the same campaign.
Started with 3 players running 2 PCs each.
7 adventures in, one player left (moved out of town) and we put the game on hold. A year later, 3 more players join coming out of a campaign that had just sunk (one was its DM), and we reboot.
Adventures 1-4 are intended to be something of an adventure path but after adv. 4 they bail completely; adventures 5-11 are another and it was vaguely completed. Adventure 12 is a stand-alone module with very limited connection to the greater story (though I shoe-horned some in after the fact).
So, 5 more adventures, down another player - one of the three who joined - but we're gathering new players like a rolling snowball. I'm up to 7 total, with 2 more knocking on the door...so I split the game. 4 players in one side, 5 in the other, two parties, and away we go. The original 2 players (still each running one of their original PCs along with various replacements for the other) both go in Party B.
4 adventures later for the 'A' group (all stand-alone) and 3 for 'B' (also all stand-alone, and one on a different world with a guest DM) and they re-unite for a 2-session mass adventure as a 31-character party 'C' (DM note: what a nightmare *that* was to run!) that ties off the previously-abandoned story from adventures 1-4. Oh, and party B has another player now, so 5 and 5.
At this point, the players re-organize their PCs into three groups; players and characters swap all over the place. Note that the same 2 original players are still running their same 2 PCs, though with a constantly-changing support cast behind them. A few other long-term 'star' characters are also arising by now.
So, off into the wild again. One party, 'D', goes into a series of stand-alone adventures having little to do with any storyline at all. A second, 'E', goes into a loosely-connected 3-adventure series. And the third, 'F', does one adventure and then disbands; with its characters occasionally drifting into other parties for ages thereafter.
The next big batch of changes comes when 2 PCs get married; their wedding is an excuse for lots of characters to meet - and switch parties. By now, the parties are all loosely allied in a single adventuring Company and have a base of operations - a Company-owned castle.
Both parties go off on adventure paths - one a 4-adventure, the other ends up as 9 but not all in a row - see below. The party on the 4-adventure path reorganizes itself (players come and go, again) then goes out on some stand-alones. And those same 2 PCs are still going...
The next big shake-up comes when by sheer chance just about everyone is at the castle, and it gets attacked. Lots of people switch parties even though one party is in mid-path of a tight series.
After this, it gets messy enough I'm not sure I can describe it here, but there's parties coming and going all over the place for a while including one that intentionally walked into to Niflheim (Hel's realm) and then never came back. But this time, every party except the Niflheim group is acting on or because of the same story line - an invasion of Giants - though from different angles and with different goals. And players and characters continue to come, go, return, etc. throughout.
Eventually, it shakes down to 2 parties each on unrelated adventure paths to finish out. Of the 2 long-standing PCs, one is now dead (though its player is still in the game) and the other has no player but is still active as what we call a QPC, or quasi-player character - it's my SO's, she still lobbed in instructions from time to time.
And then, being mostly out of story ideas for that game and wanting to do a fairly serious rules shakedown, I shut 'er down.
Those two significant characters - Pearl and Throy - ran together for about 20 adventures but never with exactly the same surrounding party more than twice; they then split and ran in separate parties for another 10 and 8 respectively, again with a constantly-morphing group of companions.
So is that all one big campaign? I maintain that it is.
Lan-"783 sessions, 203 party member characters, 64 adventures"-efan