Ages ago, humans descended from Negroid, Caucasoid, and Mongoloid stock. Those were the first three "races". "Black" is shorthand for "dark-skinned person who has more visible negroid features than those of the other three original races", that today has very impolite ramifications because in more recent history, one group of people decided they were superior to another group of people and did some really bad things. Now, everything's all messed up.

There's not really a polite shorthand for "that guy with brown skin". We're so sensitive to those bad things that one group of people did in the past that it's considered rude to even notice a guy's skin color, even in a neutral manner. We're supposed to pretend we don't notice. You can use every descriptor under the sun to talk about someone else, but the second you mention he's a "black" guy, you get dirty looks for admitting that you notice skin color.

So someone might think that maybe we refer to nationality instead of race to avoid being offensive by saying, "African American", but a visibly "black" person of Indonesian descent who's a citizen of France is neither African nor American.

You can point and say, "Look at the blond girl", and that's okay, but "Look at the black girl" earns you dirty looks, all because this one bad group of people did some bad things in the past and now nobody can admit that anybody has different skin color ever again.