The "God" of Abraham is the "God" that Jews, Christians, and Muslims believe in. As mentioned by others, the difference is not in "Gods", it is in how the Religions perceive "God".
I agree with this, but I disagree with the supposed millions of people who see Jesus as God's human form, even in my own church there are some people who see it this way. 4 words can sum up what the trinity really means "Father, Son, Holy Spirit". Now if you can show me someone who is their own father other than southern backwater jokes etc, maybe I'll give you some credit that they are not different entities.I don't want to hear the magical he can be two places at once thing, I'm sure god can do what he/she wants when they want, but its generally assumed god created Jesus his firstborn only son and Jesus was the God referred to as the one who created the world,angels etc. From that point Jesus gave up his place in heaven to be a mortal man and God sent him down as a seed in Mary's virginal pregnancy, it's not like god created him in that moment just to die for our sins, he was there way before we were. That's how I believe anyways, everyone is going to have a different opinion
As far as the OP's question it is the same God, the god of Abraham.
Did you ever do that thing in school where someone is told something at the beginning of the line and it is whispered down the line till the very end of the class, and its always at least a little different from what it started at and is usually quite a bit different, That is why there are differences in the way the books are written, with the exception of how Jesus is perceived. In the end though it is up to you to decide how you actually believe so if you (OP) think he is the same god after seeing all the differing opinions listed here and elsewhere then that is what he is to you. It is all an Ideal, God is real don't get me wrong, but you have to create your own path to see him for what he really is to you.