What are the symptoms of a slipped disc and a herniated disc?

The same: Slipped disc is a layman's term for a disc herniation. Most have no symptoms and are seen fairly frequently on imaging studies. Symptoms can range from pain in the spine , in the extremities, numbness, tingling, weakness & bowel/bladder problems . If at a thoracic or cervical level maybe gait, balance or spasticity issues as well as dexterity problems. This is known as a myleopathy.

Referred pain...: Radiating pain to a well defined area of a single extremity is typical for this problem, if it's in the cervical or lumbar spine. It could also cause weakness and numbness. If the disc herniation is central and large, it could affect both sides of the body. It will often feel like knee or shoulder pain, but there is no history of a knee or elbow injury.

Synonyms: The terms bulging disk, slipped disk, herniated disk are roughly the same idea that they disc has moved out of place where it should be and possibly compressing nerve or spinal cord. Typically though herniated disk signifies a slight increase in severity of pathology over a bulging disc. It gets a little more specific if terms like disc protrusion and disc extrusion come into the mix.