Now, whether the Abrahamic religions consider their God to be one and the same is a philosophical question. It depends on what "the same" means. Each of them claims to refer to the same entity, at least from a historical (or archaeological) point of view; but some followers of the different Abrahamic religions might object to each other's representations of God and deem them "not the same." A theological case can be made that they are ultimately distinct (I find it to be weak, but it's been argued). But, nominally, they are the same entity despite differences in characterization (and I believe this is the prevalent view).