What is the difference between race and ethnicity?
Both race and ethnicity are social constructions. However, the latter is a connection forged on one's sense of belonging to a particular country (i.e., nationality), as well as a shared language, cultural traditions, and ancestral lineage. Groups of people may live within the same borders but may not share a common ethnic identity. Ethnic difference exists in presumably homogeneous countries, such as China.
Race is an idea of human difference born out of a group's shared physical traits (e.g., hair color, eye color, skin color) and ancestral lineage. Biologically, there is no such thing as race. Our physical differences developed as a result of adaptation and natural selection. For example, Northern Europeans with blond hair and blue eyes developed these traits so that their bodies could absorb Vitamin D from sunlight more efficiently, due to the lack of direct sunlight in countries such as Germany or Denmark. However, the natives of these countries are still, like all human beings, descended from a common ancestor in prehistoric Central Africa: Mitochondrial Eve, the veritable mother of the entire human race.
In the eighteenth century, pseudosciences emerged which helped to establish the idea of separate races based on certain physical traits, such as skull size (e.g., craniometry). Notions of the "inferior" intelligence and character of some groups (e.g., Africans) versus the "superior" intelligence and character of other groups (e.g., Europeans) emerged at this time, as did the designation of European peoples as "Caucasian," a moniker based on the belief that all European peoples originated in the Caucasus.
Genetically, we can identify ethnicity. Race is a bit trickier. With the popularity of genetic testing, people are finding that their lineages are a bit more complicated than they may have believed. For example, people who appear to be primarily of African descent sometimes find, through DNA testing, that they have more ancestors from European countries than from African ones. Famously, the historian and genealogist Henry Louis Gates, Jr. discovered this truth about himself through genetic testing.
Now, one would think that a man who discovers that more than half of his ancestry is European would identify as such. Yet, the fact remains that Gates appears to be a black man. The assumption of one's race is based mainly on appearance —not origins or genetic lineage. Ethnicity can help to determine race, but it is not a decisive factor.