Regarding the subject of whether Christians and Muslims speak of the same God, to begin with, the word “Allah” originally came from the Aramaic, which was the common language in Palestine at the time of Christ. It is found in the Aramaic portions of the Old Testament (OT), and was used by Christians and Jews long before Islam came on the scene. In fact, the word “Allah” would have been the word Jesus would have used to refer to God. So, “Allah” is a Christian word not a Muslim word. That is why it is used in the current Arabic Christian Bible from cover to cover.
The difficulty is that Islam later took this same word “Allah” and defined it differently. So there ends up being a similar subject with different predicates. However, the predicates in Islam are so different that they redefine the subject. This then reintroduces the starting point between Islam and Christianity as having different subjects all together. They seem to start with the same subject, but later demonstrate that they are actually speaking of two different subjects!
Here is the difference. Both Islam and Christianity believe in the existence of God and in the oneness of God. But Islam stops here! Christianity continues with at least four more specifications of God not found in Islam and even strongly rejected by it. Beyond the existence and oneness of God, Christianity believes in (1) the coming of God (incarnation), (2) the redemption of God (through the cross), and (3) all this being possible because of a wondrous and unique nature of the oneness of God (the Trinity). Not only so, but (4) there is a whole distinctive theology in the background that allows for the incarnation, redemption and Trinity.
In fact the theological foundation for the incarnation, redemption and Trinity is even found in the OT. It is the very reason why the oneness of God of the OT is very different from the oneness of God in the Quran, and exposes the primal dissimilarity between Trinitarian Monotheism and Unitarian Monotheism. The theology of the latter is so opposed to the Bible at the core!
In the final analysis, from a biblical standpoint, the Triune God is the only true God that exists!