jot down vs write

jot down and write both are verbs.

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

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

jot down (verb)	write (verb)
write briefly or hurriedly; write a short note of	communicate or express by writing
	record data on a computer
	contact in writing
	produce a literary work
	mark or trace words or symbols on a surface
	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