Today we know that Europeans are mostly descended of Ice Age survivors who holed up in three "refugia" (places not turned to desert or covered with ice sheets). That separation lasted from about 35,000 years ago to 15,000 years ago.
At least one subgroup broke off and moved to America about the peak of the ice some 20,000 years ago ~ and their descendants are still around ~ with their own unique identifying DNA sequence.
East Asians are descended from several different populations that holed up in Eastern "refugia". Further, even though Chinese and Europeans are the same people separated by about 35,000 years, they did swap girls across the vastness of Asia back during the Ice Age so we've all got 5% of each other's otherwise unique DNA sequences. The Chinese also divided into two groups, one of which is better known as the Ainu (who are closely related to the Jomon and Emeshi populations in Japan in earlier times).
The earliest people to leave the European refugia in the West went straight North to Norway and became genetically isolated from other Europeans until about 800 AD. Parts of that population moved on East over the top of Scandinavia and met up with other Europeans coming in from the South.
I think that gives you 5 distinctive "European races".
Then there are the people from the Middle East and North Africa who also moved into Europe, etc. over time.
The people in Africa are otherwise identifiably members of 13 other haplogroups! There the reasons for divergence and isolation had to do with the abominable climate in most of Africa, and physical barriers that made movement from one part to the other quite difficult until modern times 75,000 years later after the ancestors of the Europeans and Chinese had gone North!
There are mixed populations throughout South Asia ~ Indians, for example ALL (means 100%) have genes from both Persian and Andaman Islander type populations. The vast array of facial types and colors have arisen subsequent to that mixing.
All in all, as far as older definitions of "race" go, we probably have 40 or 50 of those!
My problem is trying to fit all that into such a short time span. Man developed over eons of time. To say such diverse races developed in just a couple of millennium is a bit of a stretch to me. To say a group went off to northern Europe and developed from Ice Age survivors (like what were they before) and say people of the Middle East? You have Scandinavians and then Middle Europeans developing all at the same time. Where did they come from? If initially all came from Africa, at what time did they start turning white? Where did the people who became Chinese come from? All had to come out of Africa as the current understanding suggests. If we are all decedents of Africa, then those of us in the US are all African-Americans. Right?