What is the difference between the pain felt from a slipped disc and a pinched nerve?

No difference: The pain felt from a slipped disc is the result of the disc pushing on a spinal nerve or the spinal cord. The pain is indistinguishable from pinched nerve pain. The location of the pain may be more peripheral -lower in leg or farther out in arm if pinched nerve, but the sensation is the same. Typically the pain is described as stabbing or burning. Crampy pain may be something else altogether.

They overlap: A slipped disc occurs somewhere in the spine and if it impinges upon a nerve, will impair the function of that nerve. If it leaks the pain can be significant. When a nerve is pinched, it usually doesn't hurt at the area of pinching (occasionally it does) but you might feel pain or loss of function in the areas supplied by that nerve. Any nerve can be pinched; ;not only in the spine.