Actually, you’ve missed a few terms! A herniated disc can be called a slipped disc, bulging disc, ruptured disc, or even a pinched nerve, all depending on the person. They all mean the same thing, but why there are so many names for it isn’t known.
The terms closest to herniated disc is bulging disc. Imagine the discs piled up one on top of the other. In between each disc is a gel that cushions the bones, or else they would be rubbing on each other. Through an injury, the gel can escape and leak out, putting pressure on the nearby nerves. This is what causes the pain.