brewer vs beer maker

brewer and beer maker both are nouns.

Word	Noun	Adjective	Verb	Adverb
brewer	Yes	No	No	No
beer maker	Yes	No	No	No

As nouns, brewer and beer maker are synonyms defined as:

brewer and beer maker: someone who brews beer or ale from malt and hops and water

brewer (noun)	beer maker (noun)
the owner or manager of a brewery	someone who brews beer or ale from malt and hops and water
someone who brews beer or ale from malt and hops and water