The term "black" or "African American", as far as I know coming from the States, is the preferred term by black/African Americans. History will tell you that black Americans fought for the right to be referred to as black/African Americans to abolish the "N" word.
If not black or African American, then what? If not "white", then what? I certainly don't want to be called a honky or cracker or be referred to as "caucasian"!!! Since my nationality is blended, how would I refer to my race? Here in Dubai Asians are from India, etc. In the States Asians are those whose ethnicity is from the Far East.
In the US defining terms were needed for employment as "quotas" were established and it was used to avoid job discrimination. There are many forms used in the US where you are asked your race and African American is used on the form, as is "white" and "hispanic". Several races are listed, along with "Other".
In the US it is black or white, then it comes down to ethnicity.
It's unfortunate that people are defined by the color of their skin or where they came/come from, but it's a fact of life.