The two major groups in modern Jewry are the Ashkenazim (i.e.,...

The two major groups in modern Jewry are the Ashkenazim (i.e., Eastern) and the Sephardic (i.e., Western) Jew -- but anthropologically they are clearly not the same race.

So both could not be who they claim to be if they both claim to be Israel and of the same race.There are United Nations papers concerning this matter, and one of their researchers, Raphail Patai declares,

“The findings of physical anatomy show that, contrary to popular view, there is no Jewish race (i.e., that among those who call themselves Jews). Documentation suggests that Jews living in one culture are similar anthropologically to the culture in which they live, rather than all being similar to each other in differing cultures”.