The term "Indian," in reference to the original inhabitants of the American continent, is said to derive from Christopher Columbus, a 15th century boat-person. Some say he used the term because he was convinced he had arrived in "the Indies" (Asia), his intended destination. Others say the term refers to his diary entry, in which he describes the natives as "una gente in Dios" (a people in God).
Whether from confusion or romanticism, "Indian" is a word of illusion, not a description of reality. But the word has stuck. It is commonly used by indigenous peoples of this continent to refer to themselves in a generic way, as a supplement to their real names. It is used throughout "federal Indian law," the domain of United States law concerned with rights and status of the original peoples of this land.
"Native American" is a phrase coined in the liberal years of the 1960's to replace "Indian" with a supposedly more appropriate term. Regardless of the intent, the term is no more appropriate than its predecessor. "America" is derived from Amerigo Vespucci, a 16th century Italian navigator who was once said to be the "discoverer" of the continent. How can the people who were already here be named with his name?
Other generic words are also problematic. "Native" and "indigenous" can rightfully be applied to anyone (or thing) born in a place, not only those who were born first. "Aboriginal" refers only to what was here "from the beginning," but the concept of "beginning" poses problems, too.
Perhaps the best course is to refer to a People by the name they take for themselves. Sometimes this means using a word that means "we are the only true people," but at least it does not mean using a word that means "you are who others say you are."