grab bag vs variety

grab bag and variety both are nouns.

Word	Noun	Adjective	Verb	Adverb
grab bag	Yes	No	No	No
variety	Yes	No	No	No

As nouns, variety is a hypernym of grab bag; that is, variety is a word with a broader meaning than grab bag:

grab bag (noun)	variety (noun)
a container from which a person draws a wrapped item at random without knowing the contents	noticeable heterogeneity
an assortment of miscellaneous items	a difference that is usually pleasant
	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