What is the difference between chiropractor and osteopath?

Very different. Osteopaths (do's) are fully licensed physicians who can practice in all 50 states, writing prescriptions & performing surgery, in essence, the same as their allopathic colleagues (md's). Chiropractors are not licensed physicians; they cannot write prescriptions or perform surgery. They do have a license for being a doctor of chiropractic, performing manipulative therapy. Do's also do manipulation.
Significant. Osteopaths essentially are fully qualified doctors who have a little extra training in joint manipulation and massage. They can prescribe medication, do surgery and are a good starting point for any musculoskeletal problems. Chiropractors are not doctors, cannot prescribe, and operate under an outmoded theory of disease that has been fully discredited.