Being an arab doesn't refer to ethnicity but culture. Arabs are made up of different ethnic backgrounds. People from like Saudi Arabia and Kuwait are the real ethnic arabs. In North Africa, Moroccans, Algerians, Egyptians are called arabs but by culture not because of their ethnicity. Egyptians are egyptians. Moroccans and Algerians are ethnically what is called Maghrebi/Amazigh. There are also Berbers in North Africa. Lebanese are Phoenicians. People became arabs because of the spread of Islam, their genes didn't magically become arab. For example, there are african countries that speak french and converted to Catholicism and absorbed other elements of French culture, it doesn't mean they're white french people. They are still African from Congo or wherever. Of course there have been intermarriages. The Israeli population consists of mostly europeans and eurasians like Russia. There are other Israeli jews who originate from Morocco, Iraq, Iran, Ethiopia and other parts of the world (ever heard of conversions?). There are also Muslim and Christian arabs in Israel who are the native people of that land. There was a small jewish population too before the mass jewish immigration from europe and eurasia. After saying all this, my question to you is which arab and which israeli are you referring to because there seems to be a continuing ignorant interpretation of what it means to be an arab or a jew. There's no way to compare.
Pretty good summary by somebody else