First of all, some history:
The term Allāh is derived from a contraction of the Arabic definite article al- "the" and ʾilāh "deity, god" to al-lāh meaning "the [sole] deity, God" (ὁ θεὸς μόνος, ho theos monos).[8] Cognates of the name "Allāh" exist in other Semitic languages, including Hebrew and Aramaic.[9] Biblical Hebrew mostly uses the plural form (but functional singular) Elohim. The corresponding Aramaic form is ʼĔlāhā ܐܠܗܐ in Biblical Aramaic and ʼAlâhâ ܐܲܠܵܗܵܐ in Syriac as used by the Assyrian Church, both meaning simply "God".[10] In the Sikh scriptures, Guru Granth Sahib, the term Allah, Punjabi (Gurmukhi): ਅਲਹੁ is used 46 times respectively.
The name was previously used by pagan Meccans as a reference to a creator deity, possibly the supreme deity in pre-Islamic Arabia.[11][12] The concepts associated with the term Allah (as a deity) differ among religious traditions. In pre-Islamic Arabia amongst pagan Arabs, Allah was not considered the sole divinity, having associates and companions, sons and daughters–a concept that was deleted under the process of Islamization. In Islam, the name Allah is the supreme and all-comprehensive divine name, and all other divine names are believed to refer back to Allah.[13] Allah is unique, the only Deity, creator of the universe and omnipotent.[5][6] Arab Christians today use terms such as Allāh al-ʾAb (الله الأب, "God the Father") to distinguish their usage from Muslim usage.[14] There are both similarities and differences between the concept of God as portrayed in the Qur'an and the Hebrew Bible.[15] It has also been applied to certain living human beings as personifications of the term and concept.[16][17]
In pre-Islamic Arabia, Allah was used by Meccans as a reference to the creator-god, possibly the supreme deity. Allah was not considered the sole divinity; however, Allah was considered the creator of the world and the giver of rain. The notion of the term may have been vague in the Meccan religion.[8] Allah was associated with companions, whom pre-Islamic Arabs considered as subordinate deities. Meccans held that a kind of kinship existed between Allah and the jinn.[21] Allah was thought to have had sons[22] and that the local deities of al-ʿUzzā, Manāt and al-Lāt were His daughters.[23] The Meccans possibly associated angels with Allah.[24][25] Allah was invoked in times of distress.[25][26] Muhammad's father's name was ʿAbd-Allāh meaning "the slave of Allāh"[25]
Some scholars[who?] have suggested that Muhammad used the term Allah in addressing both pagan Arabs and Jews or Christians in order to establish a common ground for the understanding of the name for God, a claim Gerhard Böwering says is doubtful.[27] According to Böwering, in contrast with Pre-Islamic Arabian polytheism, God in Islam does not have associates and companions nor is there any kinship between God and jinn.[27] Pre-Islamic pagan Arabs believed in a blind, powerful, inexorable and insensible fate over which man had no control. This was replaced with the Islamic notion of a powerful but provident and merciful God.[33]
According to Francis Edwards Peters, "The Qur'an insists, Muslims believe, and historians affirm that Muhammad and his followers worship the same God as the Jews (29:46). The Koran's Allah is the same Creator God who covenanted with Abraham". Peters states that the Qur'an portrays Allah as both more powerful and more remote than Yahweh, and as a universal deity, unlike Yahweh who closely follows Israelites.[15]
Here is a comprehensive study of the differences between Allah (Islamic God) and Yahweh (Christian God):
http://www.studytoanswer.net/myths_ch3.html#ch3-11
Here is another angle:
http://www.danielpipes.org/2714/is-allah-god
And one more:
http://www.minuteswithmessiah.com/question/notsame.html
From the link:
One of the biggest fictions about Islam is that they worship the same God as the Christians or the Jews. “Allah” may have come to mean “God,” but was originally the name of one of the minor deities of the Arabic peninsula. When Muhammed received the Qur’an he said it came from this one of the gods of the neighborhood, and claimed that he was the One God and all others were not real gods. But even if you accept that Allah is supposed to be the same God as that of the Jews or Christians, then he must have changed his whole nature in the 400 years between Jesus and Muhammed.
Several differences may serve to make the point. The God worshipped by Christians is a God of peace, history notwithstanding. Christianity advocates being at peace with all men. It advocates peaceful spreading of a gospel of grace to willing converts. Islam, on the other hand, advocates spreading the word through force, and endorses killing unbelievers. Regardless of the doctrines proposed by John Calvin, the Christian scriptures indicate that man has free will, and may choose to believe God or not. Islam teaches that God will save those he chooses to save, whether they want to be saved or not, and especially that one who obeys Allah all his life may be rejected merely because Allah chooses to reject him for no apparent reason, or simply because the person is a woman.
If they are the same person, one wonders why Allah and God can’t agree on history. The Jewish scriptures tell of Isaac as the heir of Abraham who was placed on an altar and saved at the last minute, while Islam says Ishmael was that person. The standard explanation for the difference is that the Jews corrupted the writings for their own purposes, but that Allah says it was Ishmael. That leaves a god who either changed history, or didn’t care when history was rewritten by someone else. The Isaac account dates back at least to several years before Jesus was born, according to documentary evidence. If that is so, and if Jesus was truly a prophet of Allah as it says in Qur’an, would he not correct the error, instead of perpetuating it as he did (Matthew 8:11; Mark 12:26; Luke 13:28, 20:37)? How could a prophet of Allah not correct such a gross error?
Most importantly, a Christian can not believe they are the same God because Christians believe that Jesus is the “only begotten of the Father” (John 1:14) and the “son of God” (Matthew 16:16-17). They believe that God allowed his son to die on a cross, a sinless sacrifice, so that men could be saved from their sins through faith in him. They believe that “there is no other name under heaven, given among men, whereby we must be saved.” (Acts 4:12) They believe that if God had been able to save man in any other way, surely he would have done so, but he didn’t. They (we) believe that Jesus is the Messiah, the focal point of all history, the one forward to whom all the Old Testament scriptures point and backward to whom all the New Testament scriptures point. All of this is repudiated by the Allah of Islam, who says in his Qur’an that it is error to think that one could call himself a son of Allah and that Jesus did not die on a cross. It is inconceivable to think that the God who said, “This is my beloved Son in whom I am well pleased” (Matthew 3:17) could also say “Allah is only one God; far be It from His glory that He should have a son.” (Sura 4:171)
A Christian can not believe that the God of Christianity and the Allah of Islam are one and the same. Nor do I know of any Muslim that truly believes that, either. There may be some in both groups that believe it, but in doing so they necessarily compromise their faith.
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So we can clearly see, there is at least some dispute on this matter... why do you want to pretend there isn't? Are you a practicing Muslim?