music hall vs vaudeville theatre

music hall and vaudeville theatre both are nouns.

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

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

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

Other synonyms of music hall include vaudeville theater.

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