By any definition, Jews and Arabs are the same race. They are both semitic, share a common language that diverged only 3 or 4 thousand years ago, and if you go back only a few thousand years, they share the same DNA.
One is fully Semitic while the other is a hybrid of Semite and Hamite. Not quite the same race.
It would help to clarify “any definition”, especially if one is really that sure of it. Hagar was an Egyptian, and hence a Hamite. Ishmael also took Egyptian wives.