Let’s be clear so there is no confusion – the answer is yes and no.
On the ‘yes’ side, we have the type of God, intention and Abraham, and the Quran. First, Christianity and Islam are monotheistic religions, teaching that there is only one God. While monotheists may have different ideas about God, their concept of God being one is still the same. Therefore, Christians and Muslims worship the same type of God. Second, Christians and Muslims intend to worship the same God. Since both are monotheist, there is only one God to worship. In addition, both reference they worship the God of Abraham. Third, the Quran teaches that Jews, Christians, and Muslims worship the same God. The Quran states in reference to those given the Book (Jews and Christians), “…our God and your God is One, and unto Him we surrender…” (29:46).
On the ‘no’ side is the attributes of God defined in the Bible and the Quran. Just because two monotheistic religions teach about the same type of God does not mean they are talking about the same God. For example, if a husband talks about his wife by name but gets many of her attributes wrong (tall when she’s short, blond when she’s brunet, white when she’s black), then he is really talking about a different woman. His description simply does not match the actual person who is his wife. Now the list of differences between the God of the Bible and the Quran is lengthy, but here are a few examples. In the Bible, God loves all people, including unbelievers: “For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life” (John 3:16). In the Quran, Allah does not love unbelievers: “…He does not love the unbelievers” (30:45). In the Bible, Jesus forgives sins: “If we confess our sins, He [Jesus] is faithful and just to forgive us our sins and to cleanse us from all unrighteousness” (1 John 1:9). This verses associates Jesus with God because both Christians and Muslims understand that only God can forgive sins. In the Quran, Allah does not forgive those who associate Jesus with him: “Surely Allah does not forgive that anything should be associated with Him,…” (4:48). In the Bible, Jesus is the Son of God: “…This is My beloved Son, listen to Him!” (Mark 9:7). In the Quran, Jesus is not the Son of God: “… Allah, Who has not taken a son…” (17:111). These contradictions preclude the God of Christianity and Islam being the same.
While the Quran teaches that Christians and Muslims worship the same God, it also teaches they worship different gods. It is clear due to the differences in the attributes of God that Christians and Muslims do not worship the same Creator.