closet vs cubicle

closet and cubicle both are nouns.

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

As nouns, cubicle is a hyponym of closet; that is, cubicle is a word with a more specific, narrower meaning than closet:

Other hyponyms of closet include booth, kiosk, stall.

closet (noun)	cubicle (noun)
a small private room for study or prayer	small area set off by walls for special use
a toilet in Britain	small individual study area in a library
a tall piece of furniture that provides storage space for clothes; has a door and rails or hooks for hanging clothes	small room in which a monk or nun lives
a small room (or recess) or cabinet used for storage space

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