dairy product vs milk

dairy product and milk both are nouns.

Word	Noun	Adjective	Verb	Adverb
dairy product	Yes	No	No	No
milk	Yes	No	Yes	No

As nouns, milk is a hyponym of dairy product; that is, milk is a word with a more specific, narrower meaning than dairy product:

dairy product: milk and butter and cheese
milk: a white nutritious liquid secreted by mammals and used as food by human beings

Other hyponyms of dairy product include cream, half-and-half, butter, yoghourt, yoghurt, yogurt, whey, curd, clabber, cheese.

dairy product (noun)	milk (noun)
milk and butter and cheese	produced by mammary glands of female mammals for feeding their young
	a white nutritious liquid secreted by mammals and used as food by human beings
	any of several nutritive milklike liquids

dairy product (verb)	milk (verb)
	take milk from female mammals
	add milk to
	exploit as much as possible