writing desk vs case

writing desk and case both are nouns.

Word	Noun	Adjective	Verb	Adverb
writing desk	Yes	No	No	No
case	Yes	No	Yes	No

As nouns, case is a hypernym of writing desk; that is, case is a word with a broader meaning than writing desk:

writing desk: a portable case containing writing materials and having a writing surface
case: a portable container for carrying several objects

writing desk (noun)	case (noun)
a desk for writing (usually with a sloping top)	a comprehensive term for any proceeding in a court of law whereby an individual seeks a legal remedy
a portable case containing writing materials and having a writing surface	a portable container for carrying several objects
	a glass container used to store and display items in a shop or museum or home
	bed linen consisting of a cover for a pillow
	(printing) the receptacle in which a compositor has his type, which is divided into compartments for the different letters, spaces, or numbers
	the housing or outer covering of something
	the enclosing frame around a door or window opening
	an enveloping structure or covering enclosing an animal or plant organ or part
	the actual state of things
	nouns or pronouns or adjectives (often marked by inflection) related in some way to other words in a sentence
	a statement of facts and reasons used to support an argument
	a problem requiring investigation
	a specific size and style of type within a type family
	an occurrence of something
	a person who is subjected to experimental or other observational procedures; someone who is an object of investigation
	a person requiring professional services
	a person of a specified kind (usually with many eccentricities)
	the quantity contained in a case
	a special set of circumstances
	a specific state of mind that is temporary

writing desk (verb)	case (verb)
	enclose in, or as if in, a case
	look over, usually with the intention to rob