愿意【yuànyì】

愿意 goes before a verb and says someone is willing to do it – they agree to it, or are glad to.

As a question, 你愿意…吗 is a polite invitation or request.

不愿意 for "won't"

不愿意 says someone doesn't want to and isn't going to – often "won't" or "refuses to".

愿意 or 想

想 is a wish: what you'd like. 愿意 is agreement: what you'll accept, often something someone else asked or something not much fun. Like an adjective, 愿意 takes 很 and 非常.

A verb, not a thing

愿意 is followed by a verb. Wanting a thing is 要 or 想要.

• × 我愿意一杯咖啡 → 我想要一杯咖啡