The way I differentiate between these two is using "want" and "need".
In English "need" still means "want to", but there is an added necessity.
This is apparent in the following two sentences:
I want to eat
I need to eat
You will also hear people using 需要 (Xūyào) to indicate need, so just think of 要 as a shortened version of that:
What do you need me to do
想要 is interchangeable with 想 in most uses.
Also worth noting is 要 can be used to indicate "going to":
Why do you want to break it?
Why are you going to break it?
Why do you want to go to (his/her) house?
Why are you going to (his/her) house?