pompadour vs hairdo

pompadour and hairdo both are nouns.

Word	Noun	Adjective	Verb	Adverb
pompadour	Yes	No	Yes	No
hairdo	Yes	No	No	No

As nouns, hairdo is a hypernym of pompadour; that is, hairdo is a word with a broader meaning than pompadour:

pompadour: a hair style in which the front hair is swept up from the forehead
hairdo: the arrangement of the hair (especially a woman's hair)

Other hypernyms of pompadour include coif, coiffure, hair style, hairstyle.

pompadour (noun)	hairdo (noun)
a hair style in which the front hair is swept up from the forehead	the arrangement of the hair (especially a woman's hair)

pompadour (verb)	hairdo (verb)
style women's hair in a pompadour