It was very easy to find the etymology of dentist (from French). The etymology of stomatologist was not so easy to dig. But as the suffix -(o)logy indicates, it is a Greek neologism.
This Ngram shows that indeed dentist and dentistry are largely more common that stomatologist, stomatology or oral medicine.
Some distinguish differences between the two terms, saying that stomatology is a larger medical field than dentistry:
The treatment priorities of dentistry are different from those of stomatology. For example, suppose a patient refers to a dentist to replace a lost premolar tooth. From the dentist’s and the patient’s viewpoints the replacement of that premolar tooth is the first priority; however, from a stomatologist’s viewpoint, determination of the cause of this problem and preservation of the remaining teeth are the first priorities and the second priority is the replacement of the lost premolar tooth. (read more)
However, another medical article says:
In most of the world, dentists are trained alongside
physicians and do a specialty residency in stomatology, the
medical study ofthe mouth and its diseases. The planet has around
one million den-tists and they are mostly referred to as
stomatologists. Lecturing around the world, it is very apparent
the difference this training makes in how dentists in America
practice verses how stomatologists practice.
It seems that in English, stomatologist is mainly used in scientific contexts, and dentist is so largely used because it is not restricted to scientific context. Even a child understands what a dentist is. This difference may be compared with the difference in use of the terms doctor, medical practitioner, medic, which all mean the same. Doctor is the largely used term, but in scientific literature, words like medical practitioner and medic are encountered.