The sciatic nerve is the largest nerve in the body.  It roots at the base of the lumbar and they forma long trunk down the thigh splitting into two at the knee.

True sciatica-is a result of nerve root impingement (see disc issue below) mainly due to disc injury

Piriformus sciatica-The piriformis is a small muscle located deep in the buttock, behind the gluteus maximus. It runs diagonally from the lower spine to the upper surface of the femur, with the sciatic nerve running underneath or through the muscle. The piriformis muscle helps the hip rotate, turning the leg and foot outward.  Where the piriformus muscle which sits on top of the sciatic nerve it presses on the nerve.  The prirformus muscle can be really tight and painful.  Stretching and deep tissue massage can help.