What's the difference between a protruding disk and a herniated disk?

Not too much: They both indicate a disc which may be causing pressure on adjacent nerve structures generally speaking the herniated is worse than the protruding.

Very little: Unfortunately, sometimes the terms are used interchangeably although disc bulge/protrusion means the disc is changes in shape while herniations are when the central gelatinous part pushes fully out of the fibrous covering. Just because you have a disc bulge/herniation does not mean you need surgery, see your md.