"Doctor" can be applied to all who have completed a doctoral program at a university, regardless of subject area. "Physician" applies only to those who have done their doctorate in the practice of medicine.

to my knowledge they are the same some ppl refer to MD's as physicians and DO's as doctors one is a Medical doctor (treat with drugs) one is a doctor of osteopathy (more like to treat with other methods, but will prescribe drgus as needed) it is unlikely to find a neurologist that is not an MD usually the only effective treatment of the nerves and the brain is medication. many orthopedic Dr.'s are DO's

In addition to CaptainHarley's answer, in Australia at least, some doctors are described as "Consultant Physicians" to differentiate them from those who perform surgery who are called Mister.

I knew a music leader that was sure their 'doctor' title was shown on all mentionings of their name (from their doctorate in music)... but they weren't any type of physician.

I am a doctor of philosophy and a doctor of science but I don't know anything about medicine or surgery so I am neither a physician nor a surgeon. In Britain, surgeons, from an impulse of inverted snobbery are always referred to as Mr even if they hold doctorates. (In the distant past surgeons were trained through apprenticeships, did not go to universities and consequently had no degrees, but being mastercraftsmen, when their apprenticeships were completed, they earned the title Master or Mister.) Physicians do not cut: they cure by the use of drugs; in the past they went to university, learnt a lot of classical ideas about medicine from the Greeks onward, had no idea about physiology until the middle of the 19th century, were very learned about what Hippocrates and Galen and others wrote, took degrees, but were useless for treating illness because they didn't know what caused it. In Britain the general practitioner you see when you are sick is referred to as Dr even though he probably possesses an MB (Bachelor of Medicine), and a ChB (Bachelor of Surgery). So surgeons with doctorates are referred to as Mr, physicians without doctorates are referred to as Dr, and others, usually academics with doctorates, are referred to as Dr in academic circles and Mr in real life.

I am a DrPH- a Doctor of Public Health. I am not a physician and have very different training and skills than an MD. I also have an MPH, which I mischievously refer to as Mistress of Public Health.

about half of doctors in the usa are not physicians - dentists, veterinarians, dph's, ph.d.'s, ddiv's, ed.d.'s ... i try to be careful to call folks by their appropriate title.