milk cow vs dairy cow

milk cow and dairy cow both are nouns.

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

As nouns, milk cow and dairy cow are synonyms defined as:

Other synonyms of milk cow include dairy cattle, milch cow, milcher, milker.

milk cow (noun)	dairy cow (noun)
cattle that are reared for their milk	cattle that are reared for their milk