You're referring to ethnicity not race. Race is a pretty vague and variable term depending on country but generally refers to groupings based on perceived shared physical attributes and/or shared culture.

So someone German with Nigerian ancestry refers to himself as both black (race), Nigerian (ethically) and German (nationality). Someone Malaysian with Indian ansestory who grew up in Malaysia but now lives in Australia may be brown (race), ethnically Indian, and Malaysian (nationality).

Americans tend to define race as strictly what you're perceived as by a stranger physically while many countries outside of Europe refer more to shared cultural experiences with ansestory.