write down vs set down

write down and set down both are verbs.

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

As verbs, write down and set down are synonyms defined as:

write down and set down: put down in writing; of texts, musical compositions, etc.

Other synonyms of write down include get down, put down.

write down (verb)	set down (verb)
reduce the estimated value of something	put down in writing; of texts, musical compositions, etc.
put down in writing; of texts, musical compositions, etc.	remove (cargo, people, etc.) from and leave
	put or settle into a position
	cause to sit or seat or be in a settled position or place
	go ashore
	reach or come to rest