

That’s not a contradiction, the fact that it is the page you get from searching the term is exactly their point.
Looking at the page Doctor of Osteopathic Medicine
, it even seems to point to both having the same origin (1874 USA) and later changing:
Osteopathic medicine (as defined and regulated in the United States) emerged historically from the quasi-medical practice of osteopathy, but has become a distinct and proper medical profession.
Be it resolved, that the American Osteopathic Association institute a policy, both officially in our publications and individually on a conversational basis, to use the terms osteopathic medicine in place of the word osteopathy and osteopathic physician and surgeon in place of osteopath; the words osteopathy and osteopath being reserved for historical, sentimental, and informal discussions only
Though also…
DO schools provide an additional 300–500 hours in the study of hands-on manual medicine and the body’s musculoskeletal system, which is referred to as osteopathic manipulative medicine (OMM). Osteopathic manipulation is a pseudoscience.
and from the related sources:
Mark Crislip also pointed out that DOs are using less and less osteopathic manipulation in their practice. This is a good thing, and hopefully it will eventually completely fade away. Essentially we need to distinguish between osteopathic medicine, which is mostly equivalent to standard medicine, and osteopathic manipulation, which is pure pseudoscience akin to straight chiropractic.
EDIT: Also it really sucks that things are muddied like this, I have a neck problem and there’s a potential solution that uses a precision machine but I have no idea if it’s a real procedure or just more quackery. I’ve asked a few times and got no responses or just downvotes. Though I also don’t know if the chiro places near me have it or the needed x-ray capability.
Atlas Orthogonal Percussion Instrument*. Basically it pushes the top vertebra back into alignment based on the precise angle needed.
For some background, the cause is I had whiplash many years ago. I also likely have EDS (a potential factor for the low-speed whiplash) so it’s possible even if this machine has some basis it might not be a reliable fix for me.
* often called just the first 2 words