Podiatry and Podiatric Medicine mean the same thing. Podiatric Medicine is the more accepted term now. It is the medical specialty which focuses on the treatment of foot and ankle problems by medical and surgical means. Prior to the early 1960's the profession was called Chiropody.
A podiatrist is a physician and surgeon whose scope of practice is limited to the foot and ankle. Most podiatrists have a Bachelor's or Master's degree and have graduated from a four year Podiatric Medical College. Upon graduation, the podiatrist receives a Doctor of Podiatric Medicine degree, hence the D.P.M. after his/her name. While post graduate residency training is not required to practice, most recent graduates have completed a 2 or 3 year podiatric medical and surgical residency program approved by the Council on Podiatric Medical Education (External Link). Podiatrists have DEA certificates and can prescribe Class 2-5 medications.