If a person is a medical doctor does that mean they have a doctorate?

Yes, a medical doctor (MD) has a doctorate in medicine.

Our society has used the term doctor to refer to anyone who has completed a doctoral degree in school. Thus, there are many different types of doctors, spanning many fields. Most often we associate the term doctor with certain health care professionals who have completed a doctorate level degree. Some examples of those are:

Doctors of Medicine (MD) - use medications and surgery to treat almost anything

Doctors of Dentistry (DDS) - treat problems involving teeth and gums

Doctors of Veterinary Medicine (DVM) - treat animals using medicine or surgery

Doctors of Optometry (OD) - deal with issues involving the eyes

Doctors of Podiatry (DPM) - deal with issues involving the feet

Doctors of Chiropractic (DC) - deal with issues involving the spine and neuromusculoskeletal system

But, in fact, professionals who have completed a doctorate in philosophy (PhD) are also doctors, despite not being directly involved in health care. These doctors are usually scientists and/or university professors.