Difference between 想 and 要?
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:


  我想吃饭


I want to eat


  我要吃饭


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:


  你需要我做什么？


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":


  你为什么想把它弄坏了？


Why do you want to break it?


  你为什么要把它弄坏了？


Why are you going to break it?


  你为什么想去他家？


Why do you want to go to (his/her) house?


  你为什么要去他家？


Why are you going to (his/her) house?