music hall vs theatre

music hall and theatre both are nouns.

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

As nouns, theatre is a hypernym of music hall; that is, theatre is a word with a broader meaning than music hall:

music hall: a theater in which vaudeville is staged
theatre: a building where theatrical performances or motion-picture shows can be presented

Other hypernyms of music hall include house, theater.

music hall (noun)	theatre (noun)
a theater in which vaudeville is staged	a building where theatrical performances or motion-picture shows can be presented
a variety show with songs and comic acts etc.	the art of writing and producing plays
	a region in which active military operations are in progress