put down vs drop off

put down and drop off both are verbs.

Word	Noun	Adjective	Verb	Adverb
put down	No	No	Yes	No
drop off	No	No	Yes	No

As verbs, put down and drop off are synonyms defined as:

Other synonyms of put down include discharge, drop, set down, unload.

put down (verb)	drop off (verb)
put down in writing; of texts, musical compositions, etc.	change from a waking to a sleeping state
make a record of; set down in permanent form	fall to a lower standard
put in a horizontal position	fall or diminish
remove (cargo, people, etc.) from and leave	retreat
cause to sit or seat or be in a settled position or place	remove (cargo, people, etc.) from and leave
put (an animal) to death
reduce in worth or character, usually verbally
cause to come to the ground