Technically, these terms refer to the same problem. “Slipped disc” is a bit misleading as the disc doesn’t really slip and slide around. Using either term in a search engine will bring up similar (if not the same) web links.
The disc is made up of two basic parts: the inner core called the nucleus and the outer covering called the annulus. A bulging disc refers to movement of the disc back and/or to the side toward the spinal cord or spinal nerves. The nucleus is still contained inside the annulus. Sometimes this is also called a prolapsed disc.
When there’s a tear in the annulus, the nucleus can move out past its own covering. This is referred to as a disc protrusion or herniation. The disc protrusion or herniation can come into contact and press on the nerve root. It can also send chemicals that come into contact with the nerve root causing painful back and leg symptoms.
Searching the web for medical information may be helpful. Be sure to check out any information you get for accuracy with your doctor. Sometimes wrong information is more harmful than no information at all.