Sciatica
Sciatica is a clinical term used to describe radicular pain, usually in the distribution of the L5 or S1 nerve root.  Pain is aggravated by maneuvers that put tension on the sciatic nerve.  Namely, straight leg raising, especially if the ankle is dorsiflexed.

The symptom is non-specific, but it does imply an irritative lesion along the path of the sciatic nerve or its roots.

Piriformis Syndrome
In ‘Piriformis Syndrome’ the piriformis muscle entraps the sciatic nerve deep in the buttock, giving rise to sciatica.  Theoretically, this entrapment causes pain radiating down the leg in a sciatic distribution and up into the back.  The presentation is identical to nerve root entrapment.

Proponents of this syndrome as a cause of sciatic pain say they can diagnose and treat the condition by stretching the hip into internal rotation.  Modalities such as ultrasound and massage to the piriformis area of the buttock have been proposed to reduce muscle spasm and inflammation.

The problem with this diagnosis and treatment is the lack of scientific testing of the parameters.  Until appropriate studies on the clinical presentation and effective treatment are provided, it is best to see this as a differential diagnosis of a nerve root impingement.