A bulging disc is generally a bulge of the outer covering of the disc (the annulus fibrosis) by the inner material of the disc that results in pressure of a nerve. The difference between a bulging disc and a herniated disc is a bulging disc is contained by the outer covering. Think of a bubble in a tire. The outer covering of the tire does not rupture, but there is an obvious bulge. This may cause sciatica.
An extruded disc occurs when the entire inner portion of the disc completely ruptures through the outer covering of the disc and moves freely within the spinal canal. This may cause sciatica. Surgery may be indicated in any of the disk conditions if non-operative treatment fails.
A herniated disc occurs when the gel-like inner portion of the disc ruptures or breaks through the outer covering of the disc and presses on a nerve. This may cause sciatica. A herniated disk is usually more painful and could require surgery.