drowse off vs drop off

drowse off and drop off both are verbs.

Word	Noun	Adjective	Verb	Adverb
drowse off	No	No	Yes	No
drop off	No	No	Yes	No

As verbs, drowse off and drop off are synonyms defined as:

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

drowse off (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