The answer is not as obvious as it may seem. On the one hand, we can say that, to the extent that both religions identify the God disclosed in the scriptures of Judaism as their God, then, yes, both religions worship the same deity. Both religions share some of Judaism’s scriptural narratives, though in Islam these narratives tend to be told rather differently than in the Hebrew Bible/Old Testament. Both religions revere Jesus, though in very different ways, and both have concepts of creation, sin, righteousness, and judgment. One could name other similarities as well.
So we worship the same God, though we identify many of the attributes of God differently from one another. Think of the matter this way: Imagine you and I are at a party together, and you ask me, “Which one of these people is the bishop ?” I respond that he is the man wearing a blue suit, standing next to the potted plant, and holding a glass of water. Now you know who the bishop is, and you could approach him, introduce yourself, and ask him all the questions you’ve ever wanted to ask a bishop. The thing is, while he is wearing a blue suit, he’s not standing next to a potted plant. He’s standing next to a fake plant. And he’s not holding a glass of water. He’s holding a glass of Sprite. In this case, I’ve still identified the bishop for you, but some of the descriptors I’ve used to identify him are incorrect.
This is rather like how Christians, Muslims, and Jews understand their differences in relation to the God they worship. Adherents of these religions believe that the others identify some of the attributes and actions of God correctly, but not all of them. So, for example, all three religions hold that God is eternal, transcendent, and self-revelatory. All three would say that God has given humankind moral instruction. But not all three would say that this same God is revealed most perfectly through the Quran or that God became flesh in Jesus Christ. Not all would identify Israel’s place in God’s saving work in the same way.
And this is where things get prickly. For Christians and Muslims, the attributes of God come to bear in very significant ways on their understanding of such issues as sin and judgment, atonement (or the lack thereof), eternal life, and ethical behavior. At the very heart of Christianity are the claims that God, who is Father, Son, and Holy Spirit, became incarnate, died an atoning death on the cross, and then rose from the dead. These same claims are utterly inconsistent with the Islamic understanding of Allah and his relationship to humankind. For adherents of either religion, to gloss over these distinctives is to ignore important matters that give our lives meaning and shape our worldview.
The claim, then, that Christians and Muslims worship the same God is true–but we should not overstate its significance. God is, as they say, in the details.
David F. Watson 
This is an excellent, clear, and concise statement on the validity of the popular notion that we all worship the “same god.” Thank you for it.
David thank you for the evenhanded parsing of this touchy issue. We need to both recognize and honor the common reference of both traditions to the God of Abraham, and yet recognize and honor the clear differences between what they understand about the nature of the God of Abraham, and how they worship the God of Abraham. When asked this question in my interreligious dialogue class, I simply state that the referent is the same, but the definition, practice of worship, and means of salvation are different. Islam and Christianity refer to their God as the God of Abraham and share some similar narratives connected to the God of Abraham. The referent is the same. However, how both traditions define and understand the nature of that God are clearly different with the Trinity being just the beginning of those differences. Since the understanding of the nature of God is different it follows that the practice of worship is different; the place given in worship to the person of Christ is just the beginning of such differences. Finally, since the nature of God is understood differently, then the saving acts of God, or the salvation God offers, is different; the atonement of Christ is just the beginning of such differences. Of course, I briefly referenced a few differences only from the Christian standpoint, but clearly they exist from the standpoint of Islam as well.
David thank you for the evenhanded parsing of this touchy issue. We need to both recognize and honor the common reference of both traditions to the God of Abraham, and yet recognize and honor the clear differences between what they understand about the nature of the God of Abraham, and how they worship the God of Abraham. When asked this question in my interreligious dialogue class, I simply state that the referent is the same, but the definition, practice of worship, and means of salvation are different. Islam and Christianity refer to their God as the God of Abraham and share some similar narratives connected to the God of Abraham.
The referent is the same. However, how both traditions define and understand the nature of that God are clearly different with the Trinity being just the beginning of those differences. Since the understanding of the nature of God is different it follows that the practice of worship is different; the place given in worship to the person of Christ is just the beginning of such differences. Finally, since the nature of God is understood differently, then the saving acts of God, or the salvation God offers, is different; the atonement of Christ is just the beginning of such differences. Of course, I briefly referenced a few differences only from the Christian standpoint, but clearly they exist from the standpoint of Islam as well.
I don’t believe God is in the details. God is in the essence. Religion is in the details because we want to be better and the only truth. Even among evangelicals there are many differences as to the attributes of God.
There is but One Glorious Eternal God. Because God is so vast and unknowable, different religions recognize different aspects of the same God and fight about who is right. A better analogy might be: A man is standing over there. Christianity says that he is wearing pants, Judaism says that he is wearing a shirt and Islam says he is wearing shoes. Each religion is right UNLESS they deny the truth of the other religions. FYI, I am a Baha’i and we believe in the Oneness of God, the Oneness of His Manifestations and the Oneness of Humankind.
All you have said, Mr. Sarowitz, is that your Baha’i faith holds to something significantly different than the three Abrahamic faiths. The analogy you use does not apply at all to what Dr. Watson is talking about. Jews, Christians, and Muslims who take their faith seriously would all three claim that certain doctrinal tenets of the other two religions are false (i.e., they would “deny the truth of the other religions”). The pants-shirt-shoes example does not fit because the things they would disagree about are foundational to how they believe God has been revealed. So you can hold the view you share—which is tantamount to claiming the superiority of the Baha’i faith to these other three—but don’t try to shoehorn Jewish, Christian, or Muslim belief into something acceptable to Baha’i adherents and then claim that that’s what Judaism, Christianity, and Islam actually are.