Red Indian vs Native American

Red Indian and Native American both are nouns.

Word	Noun	Adjective	Verb	Adverb
Red Indian	Yes	No	No	No
Native American	Yes	Yes	No	No

As nouns, Native American is a hypernym of Red Indian; that is, Native American is a word with a broader meaning than Red Indian:

Red Indian: a member of the race of people living in America when Europeans arrived
Native American: any member of the peoples living in North or South America before the Europeans arrived

Other hypernyms of Red Indian include Amerindian.

Red Indian (noun)	Native American (noun)
a member of the race of people living in America when Europeans arrived	any member of the peoples living in North or South America before the Europeans arrived

Red Indian (adjective)	Native American (adjective)
	of or pertaining to Native Americans or their culture or languages