A campaign is the period of time between one "reset" to another. What that means can vary from group to group, as is evidenced in this thread.
For me, it involves some level of continuity in characters. Deaths happen, and the whole party could be replaced without it becoming a new campaign. A TPK or mass retirement would most likely do it, but not necessarily. When we did RtToEE, we lost all but one PC. Because the setting/plot was a bigger focus than the characters, the campaign continued. A character-driven campaign would have ended, even if everyone brought in high-level replacements.
I ran a solo campaign for a PC, in high school. He reclaimed his father's throne and we decided to retire the character. A couple years later, I had another idea that played into the character's personality, so he un-retired and we threw in a couple other players. Some might consider that a break in a single campaign, but I don't. We'd put a ribbon on it and there was no intent of continuing until the idea struck. Similarly, I ran one campaign per school year (generally speaking) during college. Two of those years had the same party, but it was a totally new arch. It walks right up to the line, but I'd say it was a separate campaign; I wouldn't call anyone wrong who thought otherwise, though.
A couple concrete(ish) questions:
If you've read Amber, are Corwin and Merlin separate campaigns or not?
I'd say yes.
Is Avengers a separate campaign from Captain America? Hulk? Guardians?
I'd say so, but there's a good argument for Cap/Iron Man as side stories of the same campaign. The Hulk-only stuff is separate, as is the Guardians. The Guardians are clearly linked, though.