There are actually numerous types of sensory nerves, generally labelled with both Roman and Greek letters.
Take a look at this:
http://www.neuro.wustl.edu/neuromusc...other/axon.htm
While this gets complicated, the nerves can be basically divided into those that naturally have myelin coverings--all motor nerves fall into this group, as do many larger sensory nerves that sense vibration, position, mechanical touch--and those that do not (the so-called "free nerve endings"); these are either sensory or autonomic, and the sensory ones are responsible for temperature and pain sensation.
Once can have a neuropathy that damages the myelin coverings of larger nerves, OR one that damages the axons (fibers) in these nerves from the inside out. AND, one could have a neuropathy that preferentially damages the free nerve endings--the "small fibers". Such a neuropathy is by definition axonal. Some people have mixtures of all these types.
For diabetics, the most common presentation is that of a length-dependent small-fiber neuropathy, with symptoms of burning, stabbing pain and/or numbness. (These different symptoms may represent different stages of damage--though the pain of damaged nerves, which are sending erroneous signals to the brain that are being interpreted as pain, can be extreme, most neuros will say that means at least those nerves are still alive. Numb areas represent the death of fibers in that area. One can have both symptoms in the same area--some fibers damaged, some gone.)
A lot has been made in the media of diabetics with numbness, but many researchers, especially those who are working in the area of pre-diabetic, or impaired glucose tolerance, neuropathy, think that more people have pain symptoms first.