stay vs be

stay is a noun but be is not a noun.

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

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

stay: stay the same; remain in a certain state
be: have the quality of being; (copula, used with an adjective or a predicate noun)

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

stay: stay the same; remain in a certain state
be: to remain unmolested, undisturbed, or uninterrupted -- used only in infinitive form

Other hyponyms of stay include keep out, sit tight, stay together, stick together, stand, keep, stay fresh.

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

stay: continue in a place, position, or situation
be: have the quality of being; (copula, used with an adjective or a predicate noun)

stay (noun)	be (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)	be (verb)
stay the same; remain in a certain state	spend or use time
stop or halt	work in a specific place, with a specific subject, or in a specific function
overcome or allay	have an existence, be extant
fasten with stays	have life, be alive
be in a certain place and not leave	form or compose
stop a judicial process	have the quality of being; (copula, used with an adjective or a predicate noun)
dwell	occupy a certain position or area; be somewhere
continue in a place, position, or situation	be identical to; be someone or something
hang on during a trial of endurance	be identical or equivalent to
	represent, as of a character on stage
	be priced at
	to remain unmolested, undisturbed, or uninterrupted -- used only in infinitive form