"I don't want to wash clothes today."
I get the feeling that 要 is closely related to the idea of certainty of what's going to happen. 我不要洗衣服 can be translated as "I don't want to wash clothes" but must be understood as "I won't wash clothes." You don't want to, and you will not. Period. On the other hand, 想 is more of a wish. You don't want to wash these clothes, but you still have to do it. You wish you didn't have to! I hope a native can come and tell me if this is the right way to understand the distinction or if I'm overthinking it