Yes indeed. I was about to mention that, but then the concept of "race" itself is very ill defined. It is not a biologically, scientifically classifiable term. For example among the people of Africa, where the greatest genetic variation among humans exists, two black people from different regions may be genetically much more different than a white european is from a chinese. Although commonly we refer to all blacks as one race, whites as one race, east asians as one race and so on. Skin color is only skin deep, and is not really the best indicator of genetic diversity.
That is why I used the word "ethnicity", or ancestry might be suitable.