As to the term "Native American", I am a native American. That is, I was born in Rochester, Minnesota, of 100% German ancestry. "Native" refers not to one's ancestry but to "born there".
Indians are native Americans if they were not born in another country. They are aboriginal Americans, if you want to get into ten-dollar words. Of course you don't want to ignore the aboriginal Canadians and the aboriginal Mexicans and so forth.