skeleton in the closet vs skeleton in the cupboard

skeleton in the closet and skeleton in the cupboard both are nouns.

Word	Noun	Adjective	Verb	Adverb
skeleton in the closet	Yes	No	No	No
skeleton in the cupboard	Yes	No	No	No

As nouns, skeleton in the closet and skeleton in the cupboard are synonyms defined as:

skeleton in the closet and skeleton in the cupboard: a scandal that is kept secret

Other synonyms of skeleton in the closet include skeleton.

skeleton in the closet (noun)	skeleton in the cupboard (noun)
a scandal that is kept secret	a scandal that is kept secret