The modal verbs xiǎng 想 and yào 要 both indicate desire or willingness, as if saying “would like to do something” or “want to do something”.
Differences
While being used in the same context, yào 要 sounds more determined and direct, whereas xiǎng 想 implies an intention or desire that may result from consideration, which sounds less direct and more polite.
Compared to yào 要, xiǎng 想 is more compatible with the tag question kěyǐ ma 可以吗 ‘can I, may I’, to form a polite request.
Compared to bú yào 不要, the negation form bù xiǎng 不想 is more appropriate for a refusal to make it less direct and more polite.
In this use, xiǎng 想 can be modified by degree adverbs or degree adverbial phrases such as hěn 很 ‘very’, zhēn 真 ‘really’ or bú tài 不太 ‘not very’, but yào 要 cannot.