stay vs remain

stay is a noun but remain is not a noun.

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

As verbs, stay and remain are synonyms defined as:

Other synonyms of stay include rest.

As verbs, stay and remain are synonyms defined as:

Other synonyms of stay include persist, stay put, stick, stick around.

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

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

As verbs, stay and remain are synonyms defined as:

Other synonyms of stay include continue, stay on.

stay (noun)	remain (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)	remain (verb)
stay the same; remain in a certain state	stay the same; remain in a certain state
stop or halt	be in a certain place and not leave
overcome or allay	continue in a place, position, or situation
fasten with stays	be left; of persons, questions, problems, results, evidence, etc.
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