Race or ethnicity seems to signify a particular lineage concomitantly with certain physical traits and to some extent cultural heritage. Since all men descend from Adam this is a consideration of a proximate lineage. All men are one race remotely and fundamentally but proximately they are many.
This does seem to follow necessarily from the nature of living substances in that they are historical and linearly generated beings. However, in so far as race signifies a lineage it is extrinsic to a substance and therefore not a property of it, but a relation of generation. The physical traits generated in such a lineage do not seems to be properties, because they do not proceeded necessarily from one’s essence, but as part of the particular extrinsic relations of generation.
Race seems to focus more on physical traits whereas ethnicity includes cultural or national distinctions. We speak of the white race, but ethnic centers such as Little Italy or China Town.
Ethnicity then includes not only a physical heritage but also a cultural one as well. These are typically concomitant.
Mixing of races or ethnicities tends to muddle the question of race or ethnicity as there is no clear proximate lineage at the point when branches combine, though a new proximate lineage may be formed and recognized later in its development. For example, very ancient peoples who by our standards constituted ethnicities combined and segregated to form others.
All that being said, the person particularly is constituted and formed in many ways with respect to his relations to God and to others. Ethnicity and race may well play an important role in the identity of a person in the hierarchy of relations in which a person quite particularly discovers and comes to know himself, first as created by God, born of this man and woman, of this people, of this place, of this culture, with this particular traits and features, etc.
What I get out of Zippy’s discussions on such topics as this is the distinction of what Joe is and who Joe is, that is the difference between a human qua essence and qua person.