closet vs cupboard

closet and cupboard both are nouns.

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

As nouns, closet and cupboard are synonyms defined as:

closet and cupboard: a small room (or recess) or cabinet used for storage space

closet (noun)	cupboard (noun)
a small private room for study or prayer	a small room (or recess) or cabinet used for storage space
a toilet in Britain
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)	cupboard (verb)
confine to a small space, as for intensive work