music hall vs vaudeville

music hall and vaudeville both are nouns.

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

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

music hall and vaudeville: a variety show with songs and comic acts etc.

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