greasepaint vs war paint

greasepaint and war paint both are nouns.

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

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

greasepaint: a greasy substance used as makeup by actors
war paint: cosmetics applied to the face to improve or change your appearance

Other hypernyms of greasepaint include make-up, makeup.

greasepaint (noun)	war paint (noun)
a greasy substance used as makeup by actors	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