My chiropodist says that there isn't really any difference. Because of this he now calls himself a podiatrist/chiropodist.
I think he said podiatrist is an American term which seems to have been adopted.
Podiatry or podiatric medicine is a branch of medicine devoted to the study of diagnosis, medical and surgical treatment of disorders of the foot, ankle, and lower extremity.
They both treat and advise on the exact same problems of the feet, the only difference is the name, Podiatrist being more modern (and American) than chiropodist