Why did Nathan of Gaza, the famous scholar, coin the term Ashkenazi then?
Not that I believe it will make any difference, but I would be faulted for not trying.
The difference between Ashkenazi Jews and Sephardic Jews is in some minor religious observances. It’s not DNA, its not race, its not different ancestors.
Would it shock you to learn that my family became Ashkenazi after we where expelled from Spain in the 15th Century. That’s because our particular family moved into Europe where the customs were Ashkenazi. Another expelled Spanish family may have moved to North Africa and remained with the Sephardic influence.
We are all Jews, with the priestly family of Cohanim closely related in both traditions.
Here is some trivia for you, some big difference between the two traditions, Ashkenazim don’t eat corn on Passover, even though it is not forbidden -Sephardim do.