I’ve heard Christians say no, but isn’t it the same God, just different interpretations?
Unfortunately, you have to refer to aged text to find the answer.
Even though "monotheism" is defined as one God, *and* technically all three are "Abrahamic Religions" (Judaism, Christianity, and Islam,) *and finally* they all roughly came to be at a point in world history where the shift was on in terms of beliefs.. they are not the same God.
Here is the short version why... Judaism / Christianity is on one side of the fence with plenty of text suggesting at least an idea of what God is and perhaps looks like, going so far as to suggest human creation in his image. Islam pretty much goes the opposite way suggesting that God is too "distinct" from his creation thus is not describable within the confines of how a human looks.
The agnostic in me wants to say this all boils down to two kids on the playground arguing about what God should look like.
But for the purposes of this discussion it is a practical impossibility to blend the concepts of God between how Judaism/Christianity looks at this with how Islam looks at this.
Both may offer some sort of explanation as an olive branch that it is the same god and is interpretational as to the difference, but that is just a mild way of saying the other guy is wrong and on a long enough timeline someone will end up dead over the argument.
One truth across just about all religions, especially the Abrahamic three, is they hate competition. Kinda hard to say this is just an interpretation difference when all sides in the debate are willing to engage in division, hatred, killings, warfare, and honestly just complete lunacy to prove they are right.