Is there a difference between a cortisone shot and a epidural injection for pain?

Well. Technically no difference, they are probably the same. However, if the cortisone injection is not done under an x-ray machine (fluoroscopic c-arm) then it could be that the cortisone injection may be just that an injection into the muscle like a trigger point injection. Speak with your doctor to get clarity about what you will be getting.
May be the same. An epidural injection just indicates where the injection is delivered, this is typically what is meant by a cortisone injection, although cortisone injections can also be placed in muscle and joints.