writing desk vs desk

writing desk and desk both are nouns.

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

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

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

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