woman's hat vs millinery

woman's hat and millinery both are nouns.

Word	Noun	Adjective	Verb	Adverb
woman's hat	Yes	No	No	No
millinery	Yes	No	No	No

As nouns, woman's hat and millinery are synonyms defined as:

woman's hat (noun)	millinery (noun)
hats for women; the wares sold by a milliner	hats for women; the wares sold by a milliner
	shop selling women's hats