Islam shares in the monotheistic tradition preceding it in Christianity and Judaism -- the orthodox muslim belief is that יהוה of the Torah is God who revealed the Quran to Muhammed (and Moses, David, Jesus, and others were prophets before him), but the texts of the Torah and of the New Testament have been distorted.

So, yes, Allah is the Jewish and Christian god. If you want to suggest that both Allah and the christian god exist as separate divine beings, that's quite an interesting suggestion, but not supported by either religion.