I'd say this is exactly where the LLMs problems with it comes from. For most of us outside of the US and even a lot of people there, it's exactly that - a caricature of a lower class black person. However for many people it's a legit dialect of English they speak every day.

I don't live in America either, but I went on a cruise once and there were many Americans, including a black American couple who were very obviously urban. By which I mean, the wife wore high heels and a tight jeweled mini-skirt on a sea-kayaking excursion...clearly signalling that she hadn't spent much time outside of a city.

Anyway, I was shocked when they spoke exactly like The Jeffersons, with all the exaggerated whooping, non-stop vernacular, and stage-like mannerisms. It was so over-the-top that I honestly thought they were play acting, but after chatting with them for a while I realized that was just how they were. They were very nice people and clearly having a great time.

I was wondering where the V went...

Apparently African American Vernacular English (said AAVE, pronouncing each letter) is just a dialect and there's a couple other that fit under just AAE? I never knew about any of those beside AAVE.

Seems to be proper name for the kind of language a stereotypical black character in a movie would use. Can’t say about real world, since I don’t live in the USA.

AAVE is the "relaxed" English you're talking about. And with the interconnectedness of the Internet, AAVE is kind of displacing the rest.

But honestly from an etymological standpoint I think it makes sense to view AAVE as the base and then just having other flavors of it. From that link they're trying to break it down I to multiple distinct groups.

Not to be confused with African-American Vernacular English.

Aave is what I'd say is more "the kind of language a stereotypical black character in a movie would use".

African-American Vernacular English[a] (AAVE)[b] is the variety of English natively spoken, particularly in urban communities, by most working- and middle-class African Americans and some Black Canadians.[4] Having its own unique grammatical, vocabulary and accent features, AAVE is employed by middle-class Black Americans as the more informal and casual end of a sociolinguistic continuum. However, in formal speaking contexts, speakers tend to switch to more standard English grammar and vocabulary, usually while retaining elements of the non-standard accent.[5][6] AAVE is widespread throughout the United States, but is not the native dialect of all African Americans, nor are all of its speakers African American.