desk vs writing desk

desk and writing desk both are nouns.

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

As nouns, writing desk is a hyponym of desk; that is, writing desk is a word with a more specific, narrower meaning than desk:

desk: a piece of furniture with a writing surface and usually drawers or other compartments
writing desk: a desk for writing (usually with a sloping top)

Other hyponyms of desk include davenport, escritoire, secretaire, secretary, writing table.

desk (noun)	writing desk (noun)
a piece of furniture with a writing surface and usually drawers or other compartments	a desk for writing (usually with a sloping top)
	a portable case containing writing materials and having a writing surface