Jon P. answered 05/05/15
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Race and ethnicity are not the same, though they cap overlap. Race, which some scientists think isn't really a valid concept, has to do with genetics and biology, whereas ethnicity has to do with cultural environment.
Also, people can make choices about self-identification. Individuals with a mixed racial ancestry can decide whether to identify themselves as one race or another, or neither.
Here are a couple of examples...
There are many African American in the US who are black by race. There are also many blacks in Africa, or in the Caribbean, such as the Dominican Republic. These groups all have different ethnicities. Similarly, whites in the US can identify their ethnicity based on where their ancestors came from, or they can identify themselves simply as "American." Again, different ethnicities but the same race.
In the UK, there are blacks whose ancestors are African, but who identify themselves as British. This is partly due to the fact that the UK doesn't have the same history of racial problems that the US has (slavery, segregation, etc.). In a culture where there weren't strong racial barriers to assimilation, individuals of different races can more easily see themselves as part of the core culture, and ultimately the same ethnicity.