write vs put down

write and put down both are verbs.

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

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

write (verb)	put down (verb)
communicate or express by writing	put down in writing; of texts, musical compositions, etc.
record data on a computer	make a record of; set down in permanent form
contact in writing	put in a horizontal position
produce a literary work	remove (cargo, people, etc.) from and leave
mark or trace words or symbols on a surface	cause to sit or seat or be in a settled position or place
write or name the letters that comprise the conventionally accepted form of (a word or part of a word)	put (an animal) to death
write music	reduce in worth or character, usually verbally
create code, write a computer program	cause to come to the ground