Ethnicity is nothing more than a social construct; it doesn't have any objective genetic basis. So if a group of people considers themselves to be of the same ethnicity, then they are. The whole concept of ethnicity varies from one nation to another. In some parts of the world, it's very common for people to identify their ethnicity and their nationality as one and the same (i.e. China, Japan). In other parts of the world - especially in "melting pot" countries like the US - ethnicity is more often defined based on superficial traits like skin color and hair color.
One thing that I find especially interesting about the American concept of ethnicity is the Hispanic/Latino category. We are one of the only places in the world that even considers this to be an ethnic group. If you go anywhere in Latin America, people don't define themselves as Hispanic/Latino...they define themselves as white, black, Asian, Native American, or some combination of these...or by their nationality.