In actuality, they are both the same race, and they are both the same race as white Europeans, except perhaps for those Arabs who have some African blood in them, and those would be a mixture. Yemenis, for example. The idea of race is a fairly recent one, and it has always consisted of White, Asian, African or Negroid, Native American and Polynesian. There is no “semitic” race, and the ham and hagar stuff is if you take biblical genealogy literally. If you do, even then they are the same “race”, and a closely related tribe within that race.
What “actuality” are you referring to? Do you mean there is a problem with conflating the terms “race”, “tribe” and “nation” at some level?
The only way to really be pedantic about this (if one wishes) is to cite everyone’s common descent from Noah; beyond that we have his three sons Shem (Semites), Ham and Japheth. But between Jew and Arab, the only strict Semite descent is from the Jew (through Jacob’s son Judah).