lay off vs furlough

lay off is not a noun while furlough is a noun.

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

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

lay off (noun)	furlough (noun)
	a temporary leave of absence from military duty

lay off (verb)	furlough (verb)
dismiss, usually for economic reasons	grant a leave to
put an end to a state or an activity	dismiss, usually for economic reasons