choice vs possibility

choice and possibility both are nouns.

Word	Noun	Adjective	Verb	Adverb
choice	Yes	Yes	No	No
possibility	Yes	No	No	No

As nouns, possibility is a hyponym of choice; that is, possibility is a word with a more specific, narrower meaning than choice:

choice (noun)	possibility (noun)
the act of choosing or selecting	a tentative insight into the natural world; a concept that is not yet verified but that if true would explain certain facts or phenomena
the person or thing chosen or selected	a possible alternative
one of a number of things from which only one can be chosen	a future prospect or potential
	capability of existing or happening or being true

choice (adjective)	possibility (adjective)
of superior grade
appealing to refined taste