Is Muslim God really the same as that of Christian?

In Roman catholic catechism says that Muslim and Christian have the same God. But Muslim God commanded them to kill infidels like christian and other unbeliever. See what happening now in Iraq, Syria and many other Muslim countries they kill without mercy nor love. While Christian God command us to love our enemies and to do good to them. Is this just fair to Christian do nothing while they are enjoying to kill us?

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[LIST]
*]What do I say to people who say we worship the same God as Muslims?
*]How can you say that Catholics and Muslims worship the same God?
*] If Allah is a name for God, what’s wrong with Catholics praying to him?
*]Must I believe that Muslims worship my God?
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