dairy cow vs milk cow

dairy cow and milk cow both are nouns.

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

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

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

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