theatre vs music hall

theatre and music hall both are nouns.

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

As nouns, music hall is a hyponym of theatre; that is, music hall is a word with a more specific, narrower meaning than theatre:

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

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