Both 想 and 要 have the meaning of "to want" something。想 can also mean to be thinking of something, to be missing something, in general all things related to desire for something。
At times 要 can also mean "should" do something or "will" do something。 It depends on the context and what the speaker and listener both understand。
But, usually they are both fine to use as 'wanting' something。The negative response should be based on whichever one you use。
For example:你想喝水吗？(Do you want to drink water?)我不想喝水。 (I don't want to drink water。)要吃米饭吗？(Do you want to eat rice?)我不要。 (I don't want to。
) 。
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