Technically the race of what is commonly known as Jew would be Ashkenazi
No, there are three groups, Ashkenazi (Diaspora Jews who settled in central and eastern Europe), Sephardic (Diaspora Jews who settled in Iberia and North Africa, non-Diaspora Jews who remained in the Levant), and Mizrahi (non-Diaspora Jews and those who went East to Central Asia instead of West to Europe).
No, there are three groups, Ashkenazi (Diaspora Jews who settled in central and eastern Europe), Sephardic (Diaspora Jews who settled in Iberia and North Africa, non-Diaspora Jews who remained in the Levant), and Mizrahi (non-Diaspora Jews and those who went East to Central Asia instead of West to Europe).
Thanks for going more in depth, but as I said when one says "Jew" in the Western world they really mean Ashkenazi. Which is a race.
The religion and the race are two different things technically but the overlap is so great that they are basically the same thing.