millinery vs church hat

millinery and church hat both are nouns.

Word	Noun	Adjective	Verb	Adverb
millinery	Yes	No	No	No
church hat	Yes	No	No	No

As nouns, church hat is a hyponym of millinery; that is, church hat is a word with a more specific, narrower meaning than millinery:

millinery: hats for women; the wares sold by a milliner
church hat: a fanciful hat of the kind worn by Black women for Sunday worship

Other hyponyms of millinery include cloche, picture hat, pillbox, toque, turban.

millinery (noun)	church hat (noun)
hats for women; the wares sold by a milliner	a fanciful hat of the kind worn by Black women for Sunday worship
shop selling women's hats