And campaigns can exist in board games as well as RPGs. You can play seasons in Bloodbowl or have league play in Formula De. You can have campaigns in Descent or Memoir 44. And aren't some war games like World in Flames just one massive campaign?
But I have been told in no uncertain terms terms that a legacy game is distinct from a campaign. A legacy game requires you to actually physically change the game. Write on the pieces, rip up cards, add stickers, etc. You literally can never play the same physical copy of the same way twice.
I honestly don't know what I think about that idea. Turning a game into a disposable item doesn't appeal to me from a money management standpoint.
Despite that, Carrie and I have discussed getting Pandemic Legacy, since we both really like Pandemic. If we're going to try out a legacy game, that'd be our best choice and it could be a fun family activity.
The only legacy game I've actually bought is We Didn't Playtest This: Legacies, which is both a parody of the idea as well as a fully functional application of the idea. (Although since Playtest was originally inspired by 1000 Blank White Cards, Legacies is really just returning to its roots... Holy cow! 1000 Blank Cards was a legacy game years before Risk Legacy was even thought of!)
Some friends of mine rent out a meeting room at a hotel every year and invite everyone they can to game there for the weekend. I've long thought that's the perfect environment for Playtest Legacies. Have a convention copy that keeps growing and changing every year.
Still, in my heart, I am a campaigner.