This is a common translation problem. In German Doctor/Dr. is a synonymon for the Ph.D. Degree.
As all over the world you can get it many univesity subjects.

The Dr.med. in Germany is - compared to other Ph.D. Degrees - quite easy. So there are not many Doctors without Ph.D. Degree.

When you pass your final Examen (3. Staatsexamen) in Medicine you
are allowed to work as a "Arzt" (Medical Doctor), but you have no Ph.D. Degree.
So "Arzt" is a Profession and not a title!

Most Doctors I know do their Ph.D. only a few years after graduating.
Then you are allowed to call yourself Dr. XXX.
You can be "Arzt" but have no Dr/PhD.

As most "Ärzte" have Ph.D degree the "Doctor" in German is commonly used as a synonymon for "Medical Doctor".

So "Arzt" translates into "Doctor" and Ph.D (in any subject) into "Doctor" as well.

In languages it is easier:
Italian: Dottore = Ph.D; Medico = Doctor!
(Coreect me if I am wrong!)

In some countries you finish your medical studies wiht a Ph.D. Degree so the difference is not important. In Germany (and some outher countries) you have to write a seperate thesis.