writing paper vs vellum

writing paper and vellum both are nouns.

Word	Noun	Adjective	Verb	Adverb
writing paper	Yes	No	No	No
vellum	Yes	No	No	No

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

writing paper: paper material made into thin sheets that are sized to take ink; used for writing correspondence and manuscripts
vellum: a heavy creamy-colored paper resembling parchment

writing paper (noun)	vellum (noun)
paper material made into thin sheets that are sized to take ink; used for writing correspondence and manuscripts	fine parchment prepared from the skin of a young animal e.g. a calf or lamb
	a heavy creamy-colored paper resembling parchment