Black, African American, or what?

So my college room mate today asked me what the difference was between Black (colored) and African American? In her class “Ways of Seeing” the class mainly sided with Black is a color, which refers to the color of a persons skin, and that African American is a race. My room mate agrees. This got us on the topic of things such as putting your race down on paper. Usually the choices range from Caucasian, African American, Hispanic, etc. My room mate has always been told to put down African American, even though when tracing her roots she has no relatives with African heritage. She has Native American, White, and West Indie. I also know someone else who is Egyptian who can not apply for African American scholarships or put African American on paper work. Why is this?