Judaism, Christianity, and Islam are all monotheistic religions; that is, each asserts that only one God exists. Case closed ~ pretty much...

Of course, each of the three teaches/preaches a distinctly different vision of that One God; indeed, each of the three includes differing factions (sects) who disagree among themselves about the nature of God, and who each claim that they have exclusive access to the "truth" about the Divine.

People of different religions think and behave quite differently when they purport to be "serving God" or following His directives. So, in that sense, each group believes in a God whose attributes differ from those ascribed to Him by others. But each different group believes in One God; they each simply view God quite differently from each other.

So: Theologically, all three of the great monotheistic religions worship the same God, because all assert that there is one and only one God. Practically, it makes a degree of sense to say they each pray to a different "God," because they have such different agendas, different ideas about the nature of that One God.