Do Jews, Christians and Muslims worship the same god? Is the God of the Torah the same as the God of the Bible the same as the God of the Koran?
Here's my (atheistic) take on it: God is like Batman. I don't mean that he's a superhero who fights crime under the cover of darkness (though that would be pretty cool). What I mean is that the different versions of Batman are like the different versions of God. There's the Batman of the comics, the Batman of the early Batman movies and the Batman of the rebooted Christian Bale Batman movies.
In each version, certain important characteristics stay the same. Batman is always dresses up as a bat to fight crime, has a batmobile and a batcave, etc. God is always the omnipotent creator of the universe, who personally cares about humans.
But also, important characteristics change. Who killed Batman's parents and where did he learn to be an expert in hand-to-hand combat? Who was God's most recent prophet and does he care if we eat pork?
So, is God the same God? Well, in the most important aspects, yeah, pretty much. But, that doesn't mean they're interchangeable regardless of context. You can't talk about why Michael Keaton's Batman never mentions Ra's al Ghul because it's not the same continuity. Similarly, you can't ask why the Christian God allows pork when the Jewish God prohibits it.
Of course, this is approaching God as a purely fictional literary character. A real entity can't be three different versions at once. Wait a minute...
(As a sidenote, I find it somewhat interesting that Aphrodite is another god(dess) who rather different versions of herself.)