Where I'm from, people usually say
想 is more for "to think", and
要 has a flavor of "to need/require", though it really all depends on the context.
想要 mixes the two meanings, kind of like "to want" has both "desire" and "necessity".
I am thirsty. I want/need to drink water.
I need to take this course to graduate.
This dish looks delicious. I want to order this dish.
Do you want to go to Beijing?