"y do they have the same Bible"
Christianity is a direct descendant off of Judaism. Jesus was a Jew, remember that. The Old Testament was written by Jews yes...but before the time of Christ. Now, here comes the kicker...the Old Testament foretold Jesus' coming and all the miracles he would perform as well as the end of days. How can you believe in the New Testament without knowing the prophecy of the Old??? You can't, it's like trying to understand Quantum physics with absolutely no study or background.
The Old Testament is a precursor to Christianity...we wouldn't have Christianity if not for the Jews. Again, the Old Testament serves as a base to build a foundation (the doctrine of the New Testament) upon.
Based on your thinking, the Protestants should have a separate Bible, well, the Mormons have tried and failed. It has been proven historically and theologically wrong 33 times. Each of those times it's been rewritten to suit the "new-found knowledge". BTW, and this is off-topic, the founder of Mormonism, I am completely drawing a blank on his name :scream_cat: :confused:, has been proven, through historical documentation to be crazy.
Anyway, back to the original topic...
Jews, Muslims, and Christians = Same God, different views of Jesus, the Messiah, and Muhammed.