Answer:
No. The two medical degrees in the US are separate doctoral degrees, offered by separate training institutions. A Doctor of Osteopathic Medicine (D.O.) has trained at a different type of medical school than a Doctor of Medicine (M.D.) has. However, in the USA since 1980, there is little difference in the medical training, licensing, and medical practices of a D.O. and an M.D. The two medical degrees in the US are professionally equivalent.
Osteopathic medicine as a practice is, today, nearly indistinguishable from allopathic medicine. Historically, Doctors of Osteopathy have been trained to place a greater emphasis on the importance of the musculo-skeletal system and normal body mechanics as central to good health, and on the holistic approach to a patient's care. However, these historical differences have mostly fallen by the wayside today.
One historical issue of contention has been Osteopathy's use of Manual Manipulation (OMM) of the spine and joints in the treatment of diseases and disorders, which was derided by the mainstream medical community as ineffective and even charlatan. D.O.'s in the USA, especially younger doctors, now rarely use OMM. In the USA, what used to be referred to as Osteopathy is now called Osteopathic Medicine, indicating the long-term move towards mainstream medical practices on the part of DO's.
Both types of medical doctors can perform essentially the same medical practices under their state licenses to practice medicine, such as prescribing medicine, performing surgery, and specialized medical care from the various specialty areas such as oncology, pediatrics, orthopedic surgery, etc. Also, like M.D.s, they can be board certified in a particular specialty or subspecialty, which requires standards of education, demonstration of competency, and ongoing continuing medical education to maintain the certification.