music hall vs vaudeville theater

music hall and vaudeville theater both are nouns.

Word	Noun	Adjective	Verb	Adverb
music hall	Yes	No	No	No
vaudeville theater	Yes	No	No	No

As nouns, music hall and vaudeville theater are synonyms defined as:

music hall and vaudeville theater: a theater in which vaudeville is staged

Other synonyms of music hall include vaudeville theatre.

music hall (noun)	vaudeville theater (noun)
a theater in which vaudeville is staged	a theater in which vaudeville is staged
a variety show with songs and comic acts etc.