What is the difference between doctor of philosophy and Doctor?

A person who succeeds in earning a Masters level in their educational field becomes a "Doctor of (that field of study)". So the student may earn a Doctor of Philosophy, Doctor of Psychology etc. Here, "Doctor of" is a "Doctorate", an educational standing. These degrees earn the person to call themselves, Dr. John Smith... or John Smith, Ph.D. Note: The person would NOT use both a prefix and suffix:

WRONG: Dr. John Smith, Ph.D. -- using both is usually wrong because it is redundant; they both mean the same thing, so only one is needed.

A Doctor of Medicine, or Doctorate of Medicine, is the educational title. But to distinguish a Ph.D. doctorate from a Medical doctorate, we use M.D. which stands for Medical Doctor. Again, we can use either a prefix or a suffix to the person's name, such as Dr. John Smith... or John Smith, M.D.

WRONG: Dr. John Smith, M.D. -- using both is usually wrong because it is redundant; they both mean the same thing, so only one is needed.

Note that some physicians graduate from Osteopathic Medical Schools, rather than traditional Medical Schools. They are Osteopaths. Their suffix is D.O. So they could be called Dr. John Smith... or, John Smith, D.O.

M.D.s and D.O.s are both physicians, but the core theories of education differ. A D.O. is often referred to as a holistic physician because they view the person more as a whole--- with anatomy, physiology, psychological, social, sexual, etc. An M.D focuses more narrowly on just anatomy, physiology, and less on other aspects that make up a whole person. However, D.O.s and M.D.s are more alike than different nowadays and both treat the same conditions, illnesses, etc.