closet vs bathroom

closet and bathroom both are nouns.

Word	Noun	Adjective	Verb	Adverb
closet	Yes	No	Yes	No
bathroom	Yes	No	No	No

As nouns, bathroom is a hypernym of closet; that is, bathroom is a word with a broader meaning than closet:

Other hypernyms of closet include can, john, lav, lavatory, privy, toilet.

closet (noun)	bathroom (noun)
a small private room for study or prayer	a room (as in a residence) containing a bathtub or shower and usually a washbasin and toilet
a toilet in Britain	a room or building equipped with one or more toilets
a tall piece of furniture that provides storage space for clothes; has a door and rails or hooks for hanging clothes
a small room (or recess) or cabinet used for storage space

closet (verb)	bathroom (verb)
confine to a small space, as for intensive work