Is there a?difference between a herniated disc and a bulging disc?

Usually: There are not absolute definitions for either a herniated or bulging disc. What i may call a bulging disc another doctor might call herniated. In general though a herniated disc is actually protruding or hanging out of the normal disc space. A bulging disc is protruding less. Think of a drop of water, the bulging disc is the drop about to fall and the herniated disc is the drop that is falling.

Yes: Disc bulges are normal variants of a disc, not an issue that should cause a problem almost like the way radial tires on a car bulge a little to the sides as they contact the road. This occurs with disc loading as well. A disc herniation is an actual disruption of the disc's coating layers allowing disc material to move out of a normal position. This is a more frequent finding as we age.