A Herniated Disc or Disc Protrusion or Extrusion or Prolapse or Slipped disc all essentially mean the same thing. Part of the disc has pushed out possibly putting pressure on a nerve or creates inflammation that is putting pressure on a nerve.
Technically speaking the diference between a Disc bulge and a disc herniation is that a disc hernation involves the inner part of the disc breaking out through the outer layers.
The disc is made up of an inner gel like part called the nucleus and an outer more cartilaginous section called the annulus. So a bulge is when that annulus is pushing outward or “bulging” outward but the border is not broken. A herniating disc, that inner material actually breaks through the annulus to the outside. A common analogy is a jelly donut – the nucleus is the jelly and the annulus is the rest of the donut. If you squeeze the donut the jeely pushes toward one side bulging the donut on that side. “a bulged disc” When you squeeze that donut and the jelly comes out that’s your disc “herniation”. Either a disc bulge or herniated disc can put pressure on a nerve. Typically a herniation creates more pressure but not always.