AAVE is a linguistics label, and in fact refers to a sociolect. Sociolects are different from dialects in that which sociolect you’re using depends on context. Most people have different sociolects, for instance, I talk much differently with my friends than I do with my professors than I do with my family. Those are all examples of different sociolects. So when I “cut back on the informal speech in a formal setting” it is, in fact, doing the EXACT same thing AAVE speakers do in a formal setting. We both switch from our respective colloquial sociolects to Standard American Academic English. AAVE just happens to be a sociolect that has a more well known label (I think it has rather unique properties and is considered more noticeable than most sociolects as well, but I’m not 100% sure on that). Though I won’t deny that most people who know the term probably don’t know that they do the same thing and think it’s just a way to denote “black people speak”.