Black people in America are from many different cultures and are simply people that noticed that they had a shared experience of being excluded from institutions and even entire states.
The terminology simply comes from individuals taking initiative in the moment and saying "they treat everyone that looks like us all the same and we need umbrella terms to acknowledge our shared circumstance so that its easy to refer to ourselves". Other non-black people already had terms for us and these terms were typically also used in the pejorative. Many people consider "black" to be an affliction even today. So what you have is that some black people reject those older terms, some people try to repurpose and "take back" those older terms, some people create new terms, most terms are still in use.
These aren't scientific terms, but they do permeate into academia to convey a shared concept. So there isn't much to read into it except learning what the consensus is, and the history of why it is. But trying to merge it into the lexicon based on pattern recognition with other words will only confuse you.
but lets look at your example source of cognitive dissonance, NAACP:
The NAACP has done historically monumental things on behalf of a group of very different people that were being excluded as if they were the same. It comes from a different era and different motivated individuals taking initiative. It predates a different individual pushing “African American” much later on. That predates such rampant subsequent immigration and population growth in the US where enough people find African American to be so ambiguous to the point of ridiculous, while there are many slave descendants that take pride in the term and make it their whole identity (or have it forced on them like many black people in other English speaking countries with no American parents, this is particularly comical to me), whereas others who may also be slave descendants adopt black American or other adjectives and identifiers. With the NAACP there is no utility in changing that acronym and no need to or drive to, like a landmark. It wouldn’t surprise me if they arbitrarily did change the name on their own, but there is no talk or consensus amongst its beneficiaries to do so (unlike other landmarks).
Well, yes, this is how the group forms in the first place. It's made up of people who don't have an identity in common other than the one that's forced upon them of "non-white" by the white people discriminating against them.
Note that in countries which aren't white-majority you don't generally get a group of people holistically identifying as "people of colour", even if the same ethnicities would do so in the US. Instead you get different forms of racial discrimination.
Similarly LGBT+ merges a group of people with very different identities and practices, the primary thing they have in common is receiving the same kind of abuse from the same people.
Scott Alexander explains this as a way for upper-class people to maintain their privileges: "The whole point is to make sure the working-class white guy whose best friends are black and who marries a black woman and has beautiful black children feels immeasurably inferior to the college-educated white guy who knows that saying "colored people" is horrendously offensive but saying "people of color" is the only way to dismantle white supremacy."[0]
[0] https://astralcodexten.substack.com/p/a-modest-proposal-for-...
“Indeed, what is acceptable for white people to call African Americans and for black people to call themselves has evolved over the last century. The standard term has shifted from “colored” to “Negro” to “black” to “African American” as people sought to redefine themselves and their place in America.
Now, in 2020, “people of color” often is used to refer to the collective group of non-white Americans. It is offensive to single blacks out as “colored.” That, in part, is because of the painful segregationist history associated with the term prior to the mid-1960s. “Colored-only” restrooms and water fountains are examples of harmful relics of the Jim Crow South that black people had to fight, and die, to remove from American culture.”
https://www.chicagotribune.com/columns/dahleen-glanton/ct-da...
Scott Alexander's hypothesis explains all of that. Constant change is what makes fashion fashion, and fashion is a very effective way to discriminate between the in-group and the out-group.
https://www.npr.org/sections/codeswitch/2014/03/30/295931070...
For context, I am neither black nor American, I have little time for woke virtue-signalling and fake outrage, but I do want to be properly respectful of others whose background and sensitivities aren't necessarily like my own. With that in mind, I often find socially acceptable terminology around race confusing.
For example, take the word "color". I can understand why an umbrella term such as "colored people" could be problematic. However, if that is the case, I don't understand why "people of color" should be any more socially acceptable, nor why one of the most prominent advocacy groups still uses the former term in its name. There is so much unconstructive commentary about this particular example that it's hard to figure out what the relevant history and genuine sensitivities are here. Can you enlighten me?