Sam2, good point. The Sefarim break down society into these two groups, Edom and Yshmael.
As for the Edom business, it is confusing. How do they come to be Rome? Moreover, the Romans are referred to as Kitim, by Balaq. The ibn Ezra says, for these reasons, that Rome is not Edom.
However, I resloved the issue when I read the Sefer Hayashar (old Medrash compilation) that the Kitim fought with Edom. After being defeated a few times, the Kitim eventualy succeeded in conquering the Edomites. After that there wasn’t another Edom king and the two peoples mixed.