I'd like to suggest what might be an easier way to look at AU/AR:
What you call Alternate Universe I call Divergent Reality- where the story takes place in bookverse, but something is changed, like a death or non-death, and the story then diverges from canon, while still taking place in the same universe.
And Alternate Universe to me is where the characters are completely removed from bookverse and put in a different universe, i.e. the old west or Victorian England.