In a January 5, 2016 article, the Washington Post newspaper featured an article that announced that Wheaton College, an evangelical Christian college in Illinois, is planning to fire the associate professor of political science after she announced on Facebook that she believes that Allah and Yahweh are the same God.  In reality, her case is not that simple.  In fact, the professor in question has differed with the theological and moral values of Wheaton in a number of previous cases, and in this instance is refusing to participate in clarifying dialogue with Wheaton representatives regarding the implications of her statements.
However, the situation does position us to investigate the question, “Is Allah the same as Yahweh?”   Are they two names for the same God, or do the terms refer to different concepts of God?
The short answer is that Allah of the Qur’an is a very different idea of a deity than Yahweh of the Bible.  There are, of course, some similarities.  Both Christians and Muslims believe in one eternal God who created all that is. Both view God as all-powerful and all-knowing and ever-present.  However, there are vital differences between the concepts of God when it comes to the nature of God and the concept of the Trinity.
The “Allah” of the Qur’an is a distant, remote being who is impossible to come to know in any sense of ‘relationship’ with him.  He reveals not himself, but his will and directions to his people.  He demands obedience above all based on a proper sense of place and submission to Allah. Indeed, the word “Islam” means “submission.” The God of the Bible, of course, requires obedience as well, but that based on a relationship of love.  It is striking that Jesus, while stressing the truth of monotheism (one God) calls upon believers to “love” Him with the full expectation that obedience will spring best from love and not simply duty.
Mark 12:29-31
29 "The most important one," answered Jesus, "is this: 'Hear, O Israel, the Lord our God, the Lord is one.   30 Love the Lord your God with all your heart and with all your soul and with all your mind and with all your strength.'   31 The second is this: 'Love your neighbor as yourself.' There is no commandment greater than these."  
NIV
However, the most vital difference between Christians and the Muslim concept of god is the Christian belief that the one true God has forever existed in a Trinity.  One being of three persons, Father, Son and Holy Spirit, all fully God.
Islam, on the other hand, has as central to the faith the concept of “shirk.” “Shirk” teaches that Allah has no associates and is an eternal unity, not a trinity. For the Muslim, the concept of the deity of Christ and the Trinity itself is an example of “shirk,” a view that Muslims think of as heresy.
Trinity is however essential to orthodox Christianity.  Without the Trinity there would be no incarnation of God the Son in the person of Jesus Christ, and without the incarnation there would be no salvation from sin paid for at the cross and no hope of eternal life.
The rejection of the idea of the Trinity represents a head on collision between the God of the Bible and the idea of Allah. Islam rejects what we as Christians take as central to our faith, the fact that Jesus Christ is the only begotten of the Father. The Bible, taken as a whole, reveals that the Father is God, the Son is God and the Holy Spirit is God. Jesus is not merely a prophet as acknowledged by Muslims, He is God in human flesh in the miracle called the incarnation.  These doctrines are expressly rejected by Islam.
Jesus himself upholds the Trinity as he gives us the great commission:
Matt 28:19-20
19 Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit.
NIV
There are other differences between Christianity and Islam that spring from this essential difference. And so we must agree with the statement issued by Wheaton College on December 22, 2015 that says, “While Islam and Christianity are both monotheistic, we believe there are fundamental differences between the two faiths, including what they teach about God’s revelation to humanity, the nature of God, the path to salvation and the life of prayer.”  
I will conclude with the words of theologian R. Albert Mohler, President of The Southern Baptist Theological Seminary in Louisville, KY., as printed in a recent article on the Billy Graham Association website…
“We are living in challenging days. One of the most pressing challenges of our times is the task of speaking rightly about God.  This is particularly challenging when Christians encounter Muslims, but it is also a challenge when Christians encounter secular people in Western cultures…Our challenge is to speak truthfully about God, and the only way we can do that is to use the names that God gave himself.  The God of the Bible is not “Allah” and “Allah” is not the God of the Bible.  Any confusion about that undermines the very Gospel we preach.” 

Pastor Marc