I don't know the exact differences, but it's all based on what comes with the car. VE is lowest, then CE, then LE. My DH, who used to sell Toyotas, told me to remember it as VE = Value, CE = Comfort, and LE = Luxary. I have a Corolla CE.
LOL! I know...not much luxury in a Corolla! A friend of mine bought a LE right after I got my CE and he did have a few extras that mine does not have...so there's the luxury.