beer vs brew

beer and brew both are nouns.

Word	Noun	Adjective	Verb	Adverb
beer	Yes	No	No	No
brew	Yes	No	Yes	No

As nouns, brew is a hypernym of beer; that is, brew is a word with a broader meaning than beer:

beer: a general name for alcoholic beverages made by fermenting a cereal (or mixture of cereals) flavored with hops
brew: drink made by steeping and boiling and fermenting rather than distilling

Other hypernyms of beer include brewage.

beer (noun)	brew (noun)
a general name for alcoholic beverages made by fermenting a cereal (or mixture of cereals) flavored with hops	drink made by steeping and boiling and fermenting rather than distilling

beer (verb)	brew (verb)
	sit or let sit in boiling water so as to extract the flavor
	prepare by brewing