Actually muslim christian and jewish gods are one and the same. Muslims believe jesus and moses were prophets of god. Infact I believe moses is the most quoted in the quran, as well as jesus being quoted in the quran. There are a few fundamental differences, such as them not believing he is the son of god etc.. Just because they say allah doesnt mean its not god, allah is the arabic word for god just as elohim is the hebrew word for god. Do french people believe in a different god because they say dieu?
The reason Islam shares the same “God” as Christianity and Judaism is because mohamed ripped off Jewish history prior to Ishmael and claimed as his own.
“A few fundamental differences” is what makes them radically different - and Islam so dangerous. http://peacebyjesus.witnesstoday.org/JESUS.Vs.Muhammad.html