coat closet vs wardrobe

coat closet and wardrobe both are nouns.

Word	Noun	Adjective	Verb	Adverb
coat closet	Yes	No	No	No
wardrobe	Yes	No	No	No

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

coat closet: a closet for storing outerwear
wardrobe: a tall piece of furniture that provides storage space for clothes; has a door and rails or hooks for hanging clothes

Other hypernyms of coat closet include closet, press.

coat closet (noun)	wardrobe (noun)
a closet for storing outerwear	a tall piece of furniture that provides storage space for clothes; has a door and rails or hooks for hanging clothes
	collection of clothing belonging to one person
	collection of costumes belonging to a theatrical company