Allah actually is a seperate Deity from the Christian one. I've heard that the Christian God has a name like "Yeshwa" or "Yesha" I have no idea. So Allah and the Christian God are two seperate Gods, for me.
Judaism, Christianity, and Islam are a very interesting trio of faiths. All three can be different trees all grown from the same root, as they are all Abrahamic. IE; they all recognize their origins with the 'first prophet' of Abraham. They all worship and revere the god spoken of by Abraham, and so in the end God, Yaweh, and Allah are just different names for the same Deity
It is an interesting revelation when you dig into the history of Abraham and his sons, Isaac and Ishmael. Especially when you compare the story to modern attitudes of the three faiths towards each other. All the wars and animosity and bickering is essentially a centuries long family feud.