Small fiber neuropathy is by definition axonal--the smallest fibers are unmyelinated or only have the thinnest myelin sheathing on them (the latter are the A fibers)--but there can be axonal (as in the nerve fibers themselves are attacked, rather than their "insulation") neuropathy of larger, myelinated fibers as well. So, in sense, many types of SFN would be a subset of the larger realm of CIAP.

The Washington University neruomuscular website is good with these distinctions:

http://www.neuro.wustl.edu/NEUROMUSCULAR/naltbrain.html