lay off vs quit

lay off and quit both are verbs.

Word	Noun	Adjective	Verb	Adverb
lay off	No	No	Yes	No
quit	No	No	Yes	No

As verbs, lay off and quit are synonyms defined as:

Other synonyms of lay off include cease, discontinue, give up, stop.

lay off (verb)	quit (verb)
dismiss, usually for economic reasons	give up in the face of defeat of lacking hope; admit defeat
put an end to a state or an activity	go away or leave
	turn away from; give up
	give up or retire from a position
	put an end to a state or an activity