write on vs pen

write on is not a noun while pen is a noun.

Word	Noun	Adjective	Verb	Adverb
write on	No	No	Yes	No
pen	Yes	No	Yes	No

As verbs, pen is a hypernym of write on; that is, pen is a word with a broader meaning than write on:

Other hypernyms of write on include compose, indite, write.

write on (noun)	pen (noun)
	female swan
	a writing implement with a point from which ink flows
	an enclosure for confining livestock
	a correctional institution for those convicted of major crimes
	a portable enclosure in which babies may be left to play

write on (verb)	pen (verb)
write about a particular topic	produce a literary work