You're right! To the Romans, every Roman citizen was a Roman. There was no "genetically Roman" category. The OP's "genetic" category is indeed a "made up concep

You're right! To the Romans, every Roman citizen was a Roman. There was no "genetically Roman" category. The OP's "genetic" category is indeed a "made up concept", as you say! And the reason they made it up is the reason I stated above.