Once a learner asked me this question.
你想吃什么？What would you like to eat?
Generally in this kind of context, 想 can be considered as 'would like', 我想吃...(I'd like to eat...). So 想吃 is softer and more polite than 要吃 (want to eat...), which is more direct.
你想要什么？ What would you like? ( When talking, also with a polite tone)
想 and 要 sometimes almost mean the same thing -'want' (to do something). In this case, 要 means the person is more decided, 想 means a person is considering to do something, intends to do something.