Medically, really no difference in definition - patients tend to talk about their illnesses and doctors more about diseases. Some conditions are traditionally described as "disease" and others as "illness" and would sound wrong with the other term. Examples that spring to mind are "a flu-like illness", "autoimmune disease", "psychosomatic illness", "Alzheimer's disease".
Dorland's Illustrated Medical Dictionary:
"disease (dis·ease) [Fr. dès from + aise ease] - any deviation from or interruption of the normal structure or function of a part, organ, or system of the body as manifested by characteristic symptoms and signs; the etiology, pathology, and prognosis may be known or unknown."http://www.mercksource.com/pp/us/cns/cns_hl_d...
"illness (ill·ness) - disease"http://www.mercksource.com/pp/us/cns/cns_hl_d...
another term sometimes used with the same meaning is "sickness"
"sickness (sick·ness) - disease"
(e.g. "radiation sickness", "altitude sickness", "sleeping sickness")