brew vs beer

brew and beer both are nouns.

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

As nouns, beer is a hyponym of brew; that is, beer is a word with a more specific, narrower meaning than brew:

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

Other hyponyms of brew include kvass, mead, cassiri, spruce beer.

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

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