And you have three main types of nerve fibers - A, B, and C type. The thicker the nerve fiber, the faster it can send an electrical signal, just like with a wire. The thicker the wire, the more efficient the electricity flow. That's why the fast nerve impulses you mention that are really fast are from A fibers, the thickest which we quickly feel sharp pain and control fast reflexes.
But there is also slow, dull pain such as a toothache which goes along the C fibers which are very thin.