write vs set down

write and set down both are verbs.

Word	Noun	Adjective	Verb	Adverb
write	No	No	Yes	No
set down	No	No	Yes	No

As verbs, set down is a hyponym of write; that is, set down is a word with a more specific, narrower meaning than write:

write (verb)	set down (verb)
communicate or express by writing	put down in writing; of texts, musical compositions, etc.
record data on a computer	remove (cargo, people, etc.) from and leave
contact in writing	put or settle into a position
produce a literary work	cause to sit or seat or be in a settled position or place
mark or trace words or symbols on a surface	go ashore
write or name the letters that comprise the conventionally accepted form of (a word or part of a word)	reach or come to rest
write music
create code, write a computer program