Most Arab Jews (collectively known as the Mizrahim) now live in Israel, although there are still significant communities in Morroco, Algiers and Tunsia. The most famous Mizrahim is probably the French film director Claude Lelouche.
You don't hear too much of Arabs Jews in general. Never heard of Mizrahim. Any of them live in America?
Ever heard of the term Sephardi? They are usually called Oriental or Ladino Jews. They are from Spain, Southwest Asia, and North Africa.