Why is my campaign for Starcraft 2 at two different stages with same profile

While I have no has personal experience with this, I would guess that the saved game is saved locally on your computer, or only get uploaded to battle.net so often. I can't imagine battle.net saving every single game for every single player. So when you play on one computer you either will not see it updated on your other system for some time, or never, depending on if battle.net keeps track of your campaign progress or not.

It certainly keeps track of achievements, but beyond that I am doubtful.

What I think you're doing is that you're loading a saved game. Loading a saved game loads campaign progress as well. If you just "continue campaign" you should be in the same place on all computers.