cubicle vs closet

cubicle and closet both are nouns.

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

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

cubicle (noun)	closet (noun)
small area set off by walls for special use	a small private room for study or prayer
small individual study area in a library	a toilet in Britain
small room in which a monk or nun lives	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

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