writing pad vs pad of paper

writing pad and pad of paper both are nouns.

Word	Noun	Adjective	Verb	Adverb
writing pad	Yes	No	No	No
pad of paper	Yes	No	No	No

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

Other hypernyms of writing pad include pad, tablet.

writing pad (noun)	pad of paper (noun)
a pad of paper on which messages can be written	a number of sheets of paper fastened together along one edge