stay on vs stay

stay on is not a noun while stay is a noun.

Word	Noun	Adjective	Verb	Adverb
stay on	No	No	Yes	No
stay	Yes	No	Yes	No

As verbs, stay on and stay are synonyms defined as:

Other synonyms of stay on include continue, remain.

As verbs, stay is a hyponym of stay on; that is, stay is a word with a more specific, narrower meaning than stay on:

Other hyponyms of stay on include abide, bide, hold over.

stay on (noun)	stay (noun)
	continuing or remaining in a place or state
	(nautical) brace consisting of a heavy rope or wire cable used as a support for a mast or spar
	a thin strip of metal or bone that is used to stiffen a garment (e.g. a corset)
	a judicial order forbidding some action until an event occurs or the order is lifted
	the state of inactivity following an interruption

stay on (verb)	stay (verb)
continue in a place, position, or situation	stay the same; remain in a certain state
	stop or halt
	overcome or allay
	fasten with stays
	be in a certain place and not leave
	stop a judicial process
	dwell
	continue in a place, position, or situation
	hang on during a trial of endurance