According to the Bible, there is only one God, the One worshiped by Abraham. Other gods do not exist. Satan and his associates are imposters, God’s rivals in name only. Jews, Christians and Muslims agree on this.
This one creator God is known by various names in different languages and those who worship him in all these languages and cultures have very different ideas of who He is. So while we disagree about his nature, the fact remains that there is only one God, whom we all (Muslims, Jews and Christians) worship with greater or lesser insight into his true character and mission.
Are Muslims worshiping a “different god,” meaning a different spiritual entity? No, that is not even possible; because we do not believe a different god exists, unless we are prepared to believe that Muslims worship Satan unknowingly.
Jesus’ example towards the Samaritan woman is instructive here. He did not tell her, “you worship the wrong God.” Instead He told her: “You Samaritans worship what you do not know, we worship what we do know, for salvation is from the Jews.” And then he led her into a full understanding of who he was in comparison with that which she did not know. This is what I mean when I say that we move from common ground to higher ground.