This is actually a more difficult question to answer than you might imagine.
In the first place, one goes to chiropractic college while the other goes to osteopathy college. The main difference, however, is in how they are introduced to their particular specialism. Chiropractors and osteopaths spend between four and five years practising treatment methods and techniques, studying anatomy and medical subjects, working through conditions and then developing their clinical reasoning skills and management protocols under supervision.
The real answer is that there is a huge variance in the ways that individuals within both professions practise.
Some chiropractors practice more like an osteopath might and I know of some osteopaths who practice like “Straight” chiropractors (meaning they do not massage or focus on rehabilitation at all and only ‘adjust’ joints).
The major difference between an Osteopath and a chiropractor is that while the chiropractor is primarily focused on the spine and joints (and the muscles too, to a point), an Osteopath is also concerned with the rest of the body. He or she might treat patients with respiratory problems, digestive problems or any other number of problems that might not seem related to the spine or joints.
Typically chiropractors will use “Adjustments” , which are as specific as possible and aimed at restoring joint position and function. Osteopaths typically take a broader approach and may treat a larger area.
Both professions are highly trained at an undergraduate level and both are trained to be excellent clinicians and to care for your health first and foremost.