That’s not a contradiction, the fact that that 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.
oce@jlai.lu 8 months ago
Why do they keep a name referring to a pseudo-science then?
It is as if astrophysicists were using the name Doctor of Astrology and then claiming they are not the same as the astrology pseudoscience. Why would they do use this name then?