red man vs Native American

red man and Native American both are nouns.

Word	Noun	Adjective	Verb	Adverb
red man	Yes	No	No	No
Native American	Yes	Yes	No	No

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

red man: (slang) offensive term for Native Americans
Native American: any member of the peoples living in North or South America before the Europeans arrived

Other hypernyms of red man include Amerindian.

red man (noun)	Native American (noun)
(slang) offensive term for Native Americans	any member of the peoples living in North or South America before the Europeans arrived

red man (adjective)	Native American (adjective)
	of or pertaining to Native Americans or their culture or languages