drowse off vs doze off

drowse off and doze off both are verbs.

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

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

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

drowse off (verb)	doze off (verb)
change from a waking to a sleeping state	change from a waking to a sleeping state