There is way more groups then AAA or indie...
No, not "way more", just one - AA, and even that one's a bit of a stretch. I've seen all sorts of other bullshit terms floating around, like "AA+" or "III", and it's all just delusional hair-splitting from people with way too much time on their hands.
AAA arose as the a videogaming equivalent for film's "blockbuster", a marketing term to distinguish top-dollar flagship productions from the rank-and-file "regular" videogames. Then you got "mobile games", albeit that's just the polite term for braindead toys you distract yourself with while you wait your turn at the barber's. And then, once the industry grew to once again provide a commercial space for small garage developers, you got "indie games", which can describe anything from mobile games on PC to the videogaming equivalent of the short film, the "cheap and cheerful" segment of the industry. The "AA" term itself merely describes what we used to just call "games" without any other qualifier.
That should be enough for all practical purposes, but some people ain't content until videogaming's taxonomy looks like the tangled spaghetti of metal subgenres.