In short:
Osteopathic medicine (formerly known as osteopathy) is "a complete system of medical care with a philosophy that combines the needs of the patient with current practice of medicine, surgery and obstetrics. The emphasis is on the interrelationship between structure and function, and has an appreciation of the body's ability to heal itself." [1] Outside the United States, "osteopathic medicine" is often used interchangeably with "osteopathy".
Doctors of Osteopathic Medicine, or D.O.s, apply the philosophy of treating the whole person (a holistic approach) to the prevention, diagnosis and treatment of illness, disease and injury using conventional medical practice such as drugs and surgery, along with manual therapy (Osteopathic Manipulative Medicine or OMM).
http://en.wikipedia.org/wiki/Osteopathic_medicine
Naturopathic Medicine
Naturopathic medicine (also known as naturopathy) is a school of medical philosophy and practice that seeks to improve health and treat disease chiefly by assisting the body's innate capacity to recover from illness and injury. Naturopathic practice may include a broad array of different modalities, including manual therapy, hydrotherapy, herbalism, acupuncture, counselling, environmental medicine, aromatherapy, wholefoods, cell salts, and so on. Practitioners tend to emphasise a holistic approach to patient care. Naturopathy has its origins in the United States, but is today practiced in many countries around the world in one form or another, where it is subject to different standards of regulation and levels of acceptance.
Naturopathic practitioners prefer not to use invasive surgery, or most synthetic drugs, preferring "natural" remedies, i.e. relatively unprocessed or whole medications, such as herbs and foods. Licensed physicians from accredited schools are trained to use diagnostic tests such as imaging and blood tests before deciding upon the full course of treatment. Naturopathic Practitioners also employ the use of prescription medications and surgery when necessary and refer out to other medical practitioners.
http://en.wikipedia.org/wiki/Naturopathic
Not the same thing.