Allah is not the 'God of Muslims'?

Many non-Muslims have come to incorrectly believe that Allah is the ‘God of Muslims’ – A deity somehow different from the God of the other faiths. It should be emphasized that the term “Allah” has no implied meaning at all of an Arabian god, a Moon god or even a Muslim god. Muslims are not claiming any exclusiveness when they say "Allah". However Allah is simply the Arabic Name of the one Almighty God; the same name by which Arabic-speaking Jews and Christians, refer to God. The Allah comes from the term ‘al-ilaah’. Al is the definite article in Arabic, equivalent to ‘the’ in English, while ilaah means ‘a deity or god’. So Allah means The God. This is beautifully articulated in the first pillar of Islam which is to believe that God is One, in Arabic it would be, "La ilaha illallah" meaning "There is no god but God"