Its the same God. If the Islamic God is different than the Christian God, then we also have to say the Christian God is different from the Jewish God. The arguments for one works for the other too.

So either we do that, or we've made an error in our conception of God. Humanity has, not Christianity specifically.

One possible error is to believe that God is Good - to the exclusion of the Bad. Those are human concepts. A perfect being has no need for those categories ; what a human sees as bad can be good if you look at a larger picture, or visa versa, and even that is just a human rationalization and is completely unnecessary to a perfect being.

Another possible error is to believe that God can be limited in any way. You hear people say "God can't _____." Or "God needed to ____." Any such construction is nonsense. Getting that will require a shift in understanding Jesus, from what the churches teach. If Jesus is God, he isn't reliant on some formula of dying to do something, and it doesn't matter what some human wrote a long ass time ago. I am not denying Christ - everyone wants to jump to silly conclusions... Holding certain things constant, a different understanding must pop out.

And another possible error is to believe that God is at a specific place - in Heaven, for example. The Bible explicitly tells us both God and Heaven are within us, not a place. Islam and Judaism also make this mistake, possibly moreso.

The difference between Islam and Christianity, besides Jesus, is the acceptable conditions to do violence. Islam imagines itself to be a rebellion against oppression, and violence is acceptable in fighting oppression - but only then. Similar to Christianity, Islam also characterizes sin as oppression, and a "jihad" is meant to be an internal struggle. Obviously its not only limited to internal work.