stay vs continue

stay is a noun but continue is not a noun.

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

As verbs, continue is a hypernym of stay; that is, continue is a word with a broader meaning than stay:

Other hypernyms of stay include remain, stay, stay on.

As verbs, stay and continue are synonyms defined as:

Other synonyms of stay include remain, stay on.

stay (noun)	continue (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 (verb)	continue (verb)
stay the same; remain in a certain state	exist over a prolonged period of time
stop or halt	continue talking
overcome or allay	move ahead; travel onward in time or space
fasten with stays	allow to remain in a place or position or maintain a property or feature
be in a certain place and not leave	keep or maintain in unaltered condition; cause to remain or last
stop a judicial process	continue a certain state, condition, or activity
dwell	span an interval of distance, space or time
continue in a place, position, or situation	continue in a place, position, or situation
hang on during a trial of endurance	continue after an interruption
	do something repeatedly and showing no intention to stop