It's extremely difficult to tell the two diseases apart because the symptoms are so similar.
Both diseases involve inflammation and demyelination of nerves, in MS it occurs in the central nervous system whereas in CIDP it occurs in the peripheral nervous system. Just to confuse things, CIDP often involves the CNS, e.g. symptoms like optical neuritis.
These days if no brain or spine sclerosis (lesions) show up on MRI scans MS is almost always ruled out - after all, the disease is called multiple sclerosis. The trouble is, MS may not be such a good name, as in some instances there may be no visible sclerosis yet the nerves of the CNS still become chronically inflamed. Also, many healthy people, especially over the age of 50, have lesions in the brain.
Almost everyone with CIDP has absent reflexes in lower limbs.
There are usually elevated CSF (spinal) proteins in CIDP.
CIDP usually shows up when nerve conduction studies are carried out on the legs and arms, especially if there is axonal damage, but the main indication is nerve thickening, (indicating demyelination and remyelination) especially of the nerve roots where they leave the spine, that show up in MRI scans. Sometimes the only way to diagnose CIDP is to do a nerve biopsy, usually the sural nerve in the foot.
Compared to MS there is almost no major research carried out into CIDP, maybe because it is 8 times rarer. Nobody knows what causes either disease, although CIDP is often preceded by viral attack. There seems to be a fair amount of overlap between the two illnesses and whether you are diagnosed primarily with MS , CIDP or both may depend upon your neurology department.