variety vs music hall

variety and music hall both are nouns.

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

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

Other hyponyms of variety include minstrel show, review, revue, vaudeville.

variety (noun)	music hall (noun)
noticeable heterogeneity	a theater in which vaudeville is staged
a difference that is usually pleasant	a variety show with songs and comic acts etc.
a category of things distinguished by some common characteristic or quality
a show consisting of a series of short unrelated performances
(biology) a taxonomic category consisting of members of a species that differ from others of the same species in minor but heritable characteristics
a collection containing a variety of sorts of things