Think Christianly: Do Christians and Muslims Worship the Same God?

I came across a helpful article on this by Philosopher of Religion, Doug Groothuis:

Muslims and Christians both worship one God, and many would argue that they are the same God. Are they?
Muslims and Christians: How to Get Along?
They both believe in one personal and transcendent God who has sent his prophets into the world. They both believe in sacred writings that record the prophetic revelations. They both believe that Jesus was a prophet who was sinless and born of a virgin. And they both worship with these beliefs firmly in place. We are speaking of Muslims and Christians, whose members comprise the two largest monotheistic religions in the world.
In the wake of the terrorist attacks of September 11, 2001, Americans have become fascinated with the beliefs and practices of Islam, which is thefastest growing religion in the world, with approximately 1.3 billion adherents. Increasingly, Muslims are immigrating to the West. In various American cities, it is not uncommon to find mosques — many of them newlybuilt — and to see women in the traditional Muslim dress mingling with American women dressed quite differently.
In light of this, many Westerners wonder what do Muslims believe and why. They also question the relationship between Islam and Christianity. Do Muslims and Christians worship the same God, but merely in different ways? Should Christians seek to present their beliefs to Muslims in the hope that the Muslim might forsake Islam and embrace Christianity? Or is this simply a waste of time at best or rude at worst?
Many instruct us to be "tolerant" and to refrain from "proselytizing" anyone. In the name of tolerance, some people say that Christians and Muslims should coexist without trying to convert (or otherwise challenge) each other because "Christians and Muslims worship the same God." This, many believe, should be good enough for Muslims and Christians. Many also believe this arrangement is good enough for the God they both worship as well. If both religions worship the same God, why should they worry about each other's spiritual state?
Religion, God and Truth
If indeed Muslims and Christians worship the same God, there would be little need for disagreement, dialogue, and debate between them. If I am satisfied to shop at one grocery store and you are satisfied to shop at another store, why should I try to convince you to shop at my store or vice versa? Do not both stores provide the food we need, even if each sells different brands? The analogy is tidy, but does it really fit? Deeper questions need to be raised if we are to settle the question of whether Christians and Muslims worship the same God. First, what are the essential teachings of Christianity and Islam? Second,what does each religion teach about worshipping its God? Third, what does each religion teach about the other religion? That is, do the core teachings of Islam and Christianity assure their adherents that members of the other religion are fine as they are because both religions "worship the same God"?
In When Religion Becomes Evil (Harper. San Francisco, 2002), Charles Kimball argues that Christians and Muslims do indeed worship the same God. Kimball rightly observes that truth claims are foundational for religion. But he claims that believers err when they hold their religious beliefs in a "rigid" or "absolute" manner. So, he argues, when some Christians criticize the Islamic view of God (Allah) as deficient, they reveal their ignorance and bigotry. Kimball asserts that "there is simply no ambiguity here. Jews, Christians, and Muslims are talking about the same deity" (p. 50). This is because the Qur'an affirms that Allah inspired the Hebrew prophets and Jesus. Moreover, the Arabic word "Allah" means "God." Are Professor Kimball and so many others who echo similar themes correct? In search of a reasonable answer, we will briefly consider the three questions from the last paragraph.
Christianity and Islam: The Claims, the Logic, and the Differences
First, what are the teachings that each religion takes to be absolutely true? Although Islam and Christianity are both monotheistic, their views of God differ considerably. Islam denies (MORE)