Once you break it down it's easy to understand. Some terms describe a person's national/regional/continental heritage and origin (for example, "African"), while others describe a person's race (for example, "Hispanic"). Some terms describe both at the same time (for example, "African-American"). If you want to avoid offending people, simply refer to either their race or their nationality (depending on the context). Don't try to refer to both unless they do it first. BTW, both "Asian-American" and "Hispanic-American" are terms that I've heard used many times, though not as frequently as "African-American."