AAA has everything to do with production value, budget and marketing. But is has no bearing on quality. Plenty of expensive movies with costly effects and highly paid cast are also shit. Most AAA games are mediocre, some are great, some are crap, same as other ranges of games and gaming regardless of budgets, size of the dev team and cost of marketing, not to mention regardless of actual software sales.
I'm reminded a little bit of the age old discussion in here whether or not high sales = high quality, this is something quite different, but the OP's viewpoint seems to about as misguided, in my humble opinion. As for the distinction between A, AA and AAA, I have no idea, but on the surface it's usually really easy to tell an A title apart from an AAA, at the very least.
End of 2016 hardware sales:
Wii U: 15 million. PS4: 54 million. One: 30 million. 3DS: 64.8 million. PSVita: 15.2 million.