What is the difference between muscle spacticity and rigidity?

I’m an occupational therapy student and my neurobehaviors class deals a lot with the both of these. I can’t understand the difference though.

So far I’ve gotten that spasticity can be seen if you try to move a limb too quickly, causes a scissoring gait, and is stiffening/hypertone. I’ve got basically the same thing for rigidity: hypertonicity and that it’s both flexors AND extensors. Also different types include decerebrate or decorticate (if there are other types we haven’t learned them yet so I don’t think I need to know anything beyond that). But are both decerebrate and decorticate ONLY because of lesions to the cortex? Or does this include basal ganglia rigidty as well?