Here is one answer, translated from a post written by an American-raised Chinese on MITBBS (原贴):
I was eating lunch with a good friend (both a colleague and a classmate) a few days ago. He’s a true Englishman, having lived in England from birth through university. Although he’s now attending school with me in the United States, he naturally does so with the identity of an Englishman. Whereas I, as an ethnic Chinese person raised in the United States, have in his eyes been categorized as an “American”. And I will often correct him by saying “I’m Chinese”. This time, when the topic popped up again, he laughed and asked: “From your point of view, what is a Chinese person?”
I believe “Chinese” has three different meanings.