Why are people referring to Christian God and Muslim God as two different Gods? There is only one God. He is called by many names in different countries.
For the same reason that Jews do not call Jesus God. To a Muslim, the God that Christians believe in as God the Father is the same as the one they believe in, they just believe that the Christians have inaccurate views about the Godhood of Jesus and misunderstandings about the nature of God.
To a Christian however, the Islamic deity is not real, but rather a twisted perversion of God by a false prophet, thus, to a Christian, it is not the same.
Christians have a similar thing since they view their God the Father as the same as the Jewish God. To Christian's the Old Testament is explained as God's demonstration that humans can not save themselves, no matter how much aid they are given by God. He set a people apart, told them to kill anyone and anything that might get in their way, richly blessed them, and still they repeatedly failed to follow after God.
To Jews however, they see the law as the means to peace with God. This results in significant differences in the way that Christian's and Jews see God, though Christians view the Jewish position as simply misunderstanding the same God, while Jews would see the Christian version of God as a fabrication.