set down vs write

set down and write both are verbs.

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

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

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