I know the usual question is 'do Nintendo games count as triple A', but might as well ask the question at all three studios. 

Are games like Zelda, God of War, and Halo considered 'AAA' by the game generalalia? Is it just some of them (probably GoW and Halo because Nintendo), or none at all. 

Or does it depend on the game (Breath and Odyssey count while Let's Go doesn't, while Horizon and Spiderman count but Detroit doesn't).

AAA is just about production vales so yes a console maker’s game if high budget counts as AAA.
Halo, God of War, and even Detroit are AAA games, as are Super Mario and Zelda games. While Ori, State of Decay, Concrete Genie, and pretty much everything Nintendo makes barring Mario/Zelda are not AAA titles.

AAA means a high budget game. Most 1st party games are high budget and therefore are AAA games. There really is no hidden meaning honestly.

Edit: Beaten by a person who only just signed up today and made his first post. What a wonderful way to be beaten.

AAA(highest marketing and development budget) = Zelda BOTW, Super Mario Odyssey, Mario Kart 8 series, Smash Ultimate, Let's Go Pikachu and Splatoon 2.
AA = Xenoblade 2, Yoshi, Kirby, Fire Emblem 3H, MTA, Octopath Traveller, Mario Rabbit Kingdom Battle,
A = a lot of 3ds games and switch eshop games.

BOTW, Halo, GoW = AAA

NSMB, Ori, Everybody's golf = AA

Its all about the money man....

Pokemon despite lower dev cost its had huge Marketing budget that ecilipsed other Nintendo AAA marketing

Budget is key here, but that would put into question some of the games, especially Nintendo ones.
For example while Metroid 3d games seem AAA, it usually uses up less money than a lot of ninty AA games.

If we go by budget I'd say smash Mario kart and Splatoon as well as mainstream Pokemon count

Depends on a game's production values.

Who says Detroit is not a AAA game?

AAA is a vague description loosely connected to budget and scope.