eyeshadow vs war paint

eyeshadow and war paint both are nouns.

Word	Noun	Adjective	Verb	Adverb
eyeshadow	Yes	No	No	No
war paint	Yes	No	No	No

As nouns, war paint is a hypernym of eyeshadow; that is, war paint is a word with a broader meaning than eyeshadow:

eyeshadow: makeup consisting of a cosmetic substance used to darken the eyes
war paint: cosmetics applied to the face to improve or change your appearance

Other hypernyms of eyeshadow include make-up, makeup.

eyeshadow (noun)	war paint (noun)
makeup consisting of a cosmetic substance used to darken the eyes	full ceremonial regalia
	adornment consisting of paint applied to the face and body of certain Amerindians before a battle
	cosmetics applied to the face to improve or change your appearance