Couple things. Race is a social construct. So race in and of it self is based on European scientific racism that seeks basis in biology, but the scientific community agrees there is no race in biology. That is why Obama is considered black in America but mixed in SA. This is because race uses different social constructs. In Louisiana, which used to be a French territory, had a French system of race. Also those who fled the Hatian revolution settled there bringing that system. That is where you get Creoles, who were given social privileges based on their race above black Africans in that area. But they lost their privileges when eventually the race systems in place in the rest of America took over.
In SA, criteria for Whites vs Coloureds vs Black were based on arbitrary physical features. They would measure lip, ear, and nose sizes, use the pencil test for hair, etc to differentiate. Some families were split apart on these lines who wouldn't have been separated otherwise. My professor was telling us about knowing a kid who grew up with a Zulu family until the SA government said "wait you aren't black you're coloured." And took him from his family relocating him in the proper designated area.
Ethnicity is even more divorced from biology. An ethnic group is defined by shared historical cultural experiences, language, etc. African Americans are not African Americans because of their DNA. The DNA is mixed with numerous ethnic groups from Africa. But it's not this specific DNA admixture that makes them African American. AA's are defined as the slaves bought over to what is now the US and their descendants.
In Africa, the Tutsi and the Hutu are a great example. They are not even considered proper separate ethnic groups in the scientific community. The Belgium state made arbitrary criteria, saying if you owned more than like 10 heads of cattle you were Tutsi. They also would say Tutsi have foreheads shaped a certain way therefore they are more Eurasian and superior.
