Hi there! Black person here. Just gonna throw my two sense into the ring :3
If I were to give my two-sense on all of this, considering my ethnicity and how I was raised, I would just say that it really doesn't really matter. I think we live in a society that tries to be too politically correct in the efforts of not offending people. We end up using terms like "Black" and "African-American" to describe people of colored. And I do it all the time. There's literally nothing wrong about it.
If I were to actually give an educational-based answer combined with my experiences with now... "African-American" and "Black" are two terms that are not synonymous. It's easy to give labels to make something simple in a conversation (and by no means am I going into the "labels are completely wrong" route). Looking at it now, there are many ways to describe a colored person. What one needs to take into account is the fact that colored people are just about as ethnically deserve as a person of a fairer skin tone. I don't feel like listing all of them, but you can just about have an African-British. Tons of South Americans possess a darker skin color than what their region lets on about them. It's a fact.
What you guys classify as "Black" is just a unification of all these politically correct terms into one, casual term. Who has time to think about each and every race out there in a casual, friendly conversation? I wouldn't go out of my way to find out if a "White" person is 10% German and 60% Irish. Do they get offended? Sometimes. Same with "Black" people. So if I see a person of color down the street and I was to describe them in simplest, casual terms that anyone can understand... "Black" is the word I go for.
Is it always right? No. If you're called out, should you correct yourself? Yes.
It's the difference between connotative and denotative terms. We all love to make such a hissy fit for descriptive, connotative words when they aren't bad at all to use. Unless you're writing a formal paper, speaking to someone with authority, or something that's more on the professional side, in which that case, use the PC correct term.
If a random, caucasian stranger were to walk up to me and say, "Hey, you're black!"
I'll say, "Hey, you're white!"
I feel like we live in a society where we're looked down upon for not using the PC term. Maybe it's the thicker skin that I had to grow in.
I honestly don't care. And yes, NO self-respecting, conscientious "Black" person will get mad at you for calling them "Black". Please... stop making it such a big deal. It's okay. You can say "Black". I don't get why you're all so scared. (Of course, I'm joking) We literally do not care. As long as you don't say the N-word out of context, then we're all peachy-keen! So don't be afraid of being so damn PC correct all the time. Just don't use it as a means to better yourself or subjugate others. :3
But hey, that's my two-sense. I'm just not all that sensitive.