willing vs choice

willing and choice both are nouns.

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

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

Other hypernyms of willing include option, pick, selection.

willing (noun)	choice (noun)
the act of making a choice	the act of choosing or selecting
	the person or thing chosen or selected
	one of a number of things from which only one can be chosen

willing (adjective)	choice (adjective)
disposed or inclined toward	of superior grade
not brought about by coercion or force	appealing to refined taste