Can you tell me how is sciatica different from piriformis syndrome?

Yes: Sciatica refers to ANY cause of irritation ,injury or trauma to the sciatic nerve, at any point in its anatomic course. This can be from a stretch injury ,fall, surgery, or direct trauma. Piriformis syndrome is a irritability and spasm of the piriformis muscle ,which directly overlies the sciatic nerve. In rare cases the sciatic nerve passes through the muscle.

Piriformis Pain: The sciatic nerve runs underneath the piriformis muscle and typically does not irritate the nerve. However if the muscle is irritated or the nerve runs through the belly of the muscle (5-10% of people) it can press on the sciatic nerve and cause the sciatica type pain in the buttock region but also radiate into the leg as well. Typically stretching and nsaids are mainstay for treatment.