I don't think the notion of a god is much different. But, obviously, there are differences among the faiths. With the "Abrahamic" god, the faith was predicated on a monotheistic faith. One god. Only one god. Omnipotent and creator of all. In many of the "ancient" faiths, there were numerous gods, moreover additional half-gods or semi-deities, and with varying powers, controlling varying aspects of life.
Judaism, Christianity, and Islam viewed their god as the one, true, all-powerful supreme being. That's one of the main distinctions.
Beyond that, those religions established the notion of the one, true god having a special relationship with his "people." With some (not all) previous religions, gods acted on whims, moved humans like pawns, did what they wanted with disregard for how it affected people. While there are exceptions, for example Athena and how she watched over Athens and its citizens, in general, ancient gods acted as they wish with no reason, no mercy, no remorse. The "Abrahamic" god was/is viewed to act with reason and for his people. That's more of my opinion than anything else. He still carries wrath and vengeance. But, he also sets a standard to distinguish good and evil.
And perhaps that's one of the distinctions as well. There is a code for moral conduct. It's not just worship the gods or they'll strike you down. It's live life a certain way, do good, avoid evil.
I'm no religion expert or extremist when it comes to religion, but that's just how I see it. There are distinctions. People who believe in the "Abrahamic" god believe he's the one, true god. Whether there is enough proof of his existence is a matter of opinion. That's what faith is all about. Does it make Judaism, Christianity, and/or Islam better or more credible than any other religion? No. It's all a matter of what you believe in. But, there are definitely distinctions.