home brew vs homebrew

home brew and homebrew both are nouns.

Word	Noun	Adjective	Verb	Adverb
home brew	Yes	No	No	No
homebrew	Yes	No	No	No

As nouns, home brew and homebrew are synonyms defined as:

home brew and homebrew: an alcoholic beverage (especially beer) made at home

home brew (noun)	homebrew (noun)
an alcoholic beverage (especially beer) made at home	an alcoholic beverage (especially beer) made at home