wardrobe vs coat closet

wardrobe and coat closet both are nouns.

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

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

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

Other hyponyms of wardrobe include armoire, clothes closet, clothespress.

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