The answer is slow pain fibers
Some of the sensory impulse is carried by fast pain fiber while the other carried by slow pain fibers. Fast pain fiber is insulated by myelin sheath which make the signal could delivered at a much faster rate that fiber who doesn't. Sharp pain that caused by puncture need to have a fast response to reduce the possible damage to the body. Throbbing pain doesn't need a fast response, thus carried by slow pain fiber.