fall asleep vs drop off

fall asleep and drop off both are verbs.

Word	Noun	Adjective	Verb	Adverb
fall asleep	No	No	Yes	No
drop off	No	No	Yes	No

As verbs, fall asleep and drop off are synonyms defined as:

Other synonyms of fall asleep include dope off, doze off, drift off, drowse off, flake out, nod off.

fall asleep (verb)	drop off (verb)
change from a waking to a sleeping state	change from a waking to a sleeping state
	fall to a lower standard
	fall or diminish
	retreat
	remove (cargo, people, etc.) from and leave