Do you know the expression about a pendulum swinging back after it was swung completely one way?
There was a time when only "African-American" would do. My children have been taught that, to the point they don't know any other term - making it absurd when we were in another part of the world and they used the term there.
There are mixed opinions among those with darker skin themselves as to what to call themselves. Some will say Blacks with a capital b, some will say black wih a lower-case b, and some will prefer to use only African-American. One of my daughters has - for the first time - a black teacher and she seems to be teacher a bit more than math, which is great considering you can count the number of black kids in their elementry school on one hand. (Maybe two hands, I haven't actually tried to do it.) It seems Miss R uses the term "black people" for her 9-year-old students.
My good friend at work is black. I don't often find it necessary to refer to race, but I use "black" with her. I would use "African-American" with someone I didn't know very well, so it seems that's still the most politically correct form.
However, the black experience in the US has historically been a very different experience than in other places, so I don't see a problem having two phrases, one for the US and one for other places. if you really felt that you had to be sensitive and wanted to refer to places other than the US, then use "those of African descent."
(Note that simply "Africans" implies that they or their parents are from the US - to be an "African-American" implies generations have been here. Probably more generations than most white Americans.)
You will not fine ONE term that is always right. You will find many terms that are always wrong, however. "Colored" is considered an old-fashioned term and slighly prejudiced. Negro sounds like you're from the 1960s. And the "n-word" is considered so offensive that many people who use the "f-word" without pause but will never use the n-word.