What's the difference between shaken baby syndrome and an epileptic seizure?

Huge difference. Shaken baby syndrome is a complex of intrabrain and retinal hemorrhages from hitting, hard shaking and head banging of a (usually) crying infant to try and shut them up. It is a serious form of child abuse. Seizures are due to electrical disturbance of the brain which can be from tumors, malformations, vascular lesions or simply no known cause. It is an accident and not due to abuse.
Not the same. An epileptic seizure is relatd to electrical discahrges from an area of cells in the brain that is asynchronus. Shaken baby syndrom is from traumatic brain injury as the head is shaken back and forth with the brain being distorted and hitting against the bones of the skull.

Related Questions

I have epilepsy and am taking lamictal, but anytime im woken during the night I jerk and have seizures. I need help bc I have an infant?

Need neurologist. Lamictal is good but may not be for your type of seizures. A quality eeg including sleep would be appropriate. Your level may be low. A good neurology evaluation seems in order.
You. Should see an epileptologist--a neurologist with special training in epilepsy.

Why shouldn't people restrain an infant or child with epilepsy during a seizure?

You can break bones. The shaking an infant or child does will not hurt them. However, well, meaning people that have restrained a kid during a seizure have actually broken arms or other bones when the violent spasms occurred against their pressure to stop them.
Adults overwhelm kid. People having an epileptic seizure may move their bodies with unrestrained force. If an adult restrains the child, the difference in power of the adult may have a lever effect that might cause a fracture of an upper or lower extremity. Just move the seizing person away from the corners of furniture, place them on the floor so they will not fall if you leave to call 911. Protect the head.