There is no straight-forward answer to this question. Traditionally Osteopathy is distinguished by it's complex (holistic) approach to the body which is taken as a unit. Also Osteopathy is known for it's soft tissue work. The following are some comparisons with other hands-on practicies:

Bone-setting - an old folk method of "putting bones back into place". It does not require any special education, as one learns from experience with a master or from a family member. Because of the lack of a science base, bone-setters are almost extinct these days.

Chiropractic   - appeared at about the same time as Osteopathy. More attention is put on joints manipulation ("clicking") and less work with soft tissues. This makes the Chiropractic work harder and sometimes uncomfortable for the patient, but good for stubborn stiff joints.

Manipulative Physiotherapy - especially popular in Australia. Apart from manipulation it places greater emphasis on exercises and stretching. 

Manual Therapy - popular in Eastern Europe. It has appeared in medicine as a "proper" scientific method of hands-on treatment deriving it's base from several sources and lately it's own research. The main defect is the short duration of study and a certain "hastiness" of treatment. After doing 2 months of theory and practice a doctor can become a manual therapist, while in Osteopathy a doctor needs at least 1 year of studying and practical training.

There is a variety of other hands-on practices apart from those already mentioned: rolfing, different types of massage (classical, connective tissue, deep soft tissue massages, shiatsu, aroma-therapy and others), bio-enegry treatment and so on. All of them treat the body but do not make a diagnosis.

It is worthwhile mentioning that individual experience and talent play a great role in how the practitioner works. One can meet an Osteopath who uses hard techniques or a chiropractor who uses relatively gentle ones. A good reputation, as in ancient times, remains the main criteria of whom to go to for treatment.