possibility vs choice

possibility and choice both are nouns.

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

As nouns, choice is a hypernym of possibility; that is, choice is a word with a broader meaning than possibility:

Other hypernyms of possibility include alternative, option.

possibility (noun)	choice (noun)
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 act of choosing or selecting
a possible alternative	the person or thing chosen or selected
a future prospect or potential	one of a number of things from which only one can be chosen
capability of existing or happening or being true

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