There are two types of identity: type and individual. Take these two bottles of Lucozade. They are both the same in one way, but they are not the same in another.
The same principle applies to God. God is the same as some (not all) gods of fiction in that He is a "type" of god. That is, He is a metaphysical being with a claim to have made the universe, and maintain sovereignty over it. However, He is fundamentally different from other gods.
Using this image to further demonstrate this, let's imagine I say "I very much enjoyed that pink lemonade Lucozade". I drunk both bottles. Therefore, it is fair to say this statement refers to both bottles. However, if I say "I'm so thirsty, I wish I'd saved that second bottle for later", that can only apply to one of those bottles: the one I drank second.
When an unbeliever talks about God, they can mean any number of beings that may or may not reflect the real God. But when a Christian speaks of God, they aren't talking about any god, they're talking about the real God.
It is as illogical to claim God and Allah are the same being as it is to say these two bottles contain the same thing as a bottle of white wine. But what do you do with the God found in pseudo-Christian religions? The same thing as you do with these two bottles of Lucozade. They are the same type, but there are statements that can only apply to one.
This is especially important when it comes to apologetics. Many arguments atheists levy against "God" only apply to some gods, or maybe even only one. Take, for example, Neil Degrasse Tyson's attempt to say that science disproves God because now we know what causes natural disasters. That may work on capricious gods, like Neptune, but science itself was born out of the belief that an orderly God would create an orderly universe. Tyson's argument fails as an argument against Christianity because it's actually a powerful Christian argument against false religions.