set down vs write down

set down and write down both are verbs.

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

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

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

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

set down (verb)	write down (verb)
put down in writing; of texts, musical compositions, etc.	reduce the estimated value of something
remove (cargo, people, etc.) from and leave	put down in writing; of texts, musical compositions, etc.
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