AU has been used so interchangeably with AR that we thought the definitions above might help everyone understand it better. If we decide to go with the concept, rest assured, all members of both teams will be really clear about the difference. Maybe we all will understand it much better once we're done! Still, we'd rather use the fandom terms, but give the definitions and use them consistently.
There really is a definitive difference in their meanings: "reality" vs "universe".
REALITY: (n) (1) The quality or state of being actual or true. (2) A person, entity, or event that is actual. (3) The totality of all things possessing actuality, existence, or essence. (4) That which exists objectively and in fact. (5) The sum that is all real, absolute, and unchangeable.
Or
UNIVERSE: (n) universe, existence, creation, world, cosmos, macrocosm (everything that exists anywhere) "they study the evolution of the universe"; "the biggest tree in existence"
So when you 'diverge' or 'alternate' or 'parallel' one of these two things, you get two totally different states of being.
AU is an alternate version of the actual "world", which, in this case, is the Harry Potter Universe/Canon. So that universe is the starting point, except for this alternative, this path not taken, or similar - i.e. Snape lives to fight another day in the Battle of Hogwarts!
AR is when you get an alternate version of the "truth" or "actuality". The actual Harry Potter 'reality', or "existence" or "truth" would be alternate/parallel/divergent. For instance, a reality where no magic exists, such as our own. The Harry Potter 'reality' is one that parallels ours.