ahaha. Way to confuse things, Aucta! Those are just teams we came up with, and I admit that I like the idea of trying to take away the stigma attached to AR and learning to separate AU from AR. The minute you deviate from canon (by changing a canon event completely), you've turned a story into an alternate universe (AU) from canon. What people consider to be 'canon compliant' is the real trick, it can be so subtle, some are fooled. These stories are all set in the canon universe, only there's a deviation - you let Snape live - which makes it AU. You remember how WiP stories were canon compliant before Sirius was killed, then they became AU after the release of OotP, and people started marking them as such. Like that.
Alternate Reality runs parallel to canon - it's like a parallel universe. IE: everyone is there, but no one has magic. Or, they all live in Norway, and even if their circumstances are the same, it would still be an alternate reality to what is canon.