The BIG difference is that Christians accept Jesus Christ as their savior--The Messiah! The Jews never would accept Jesus as The Messiah. They are still waiting for The Messiah.
So, Christians began with the Jewish Torah, called it the Old Testament, put the life and words of Jesus, The Messiah, into their collection of the Torah and called it that part the New Testament. They then called the entire collection The Bible. The Jewish Torah does not have a New Testament.
Christians have a tendency to study primarily the New Testament, and miss a great deal of information that is vital to our salvation that can only be found in the Old Testament. Admittedly, Jesus does say, "Keep the Commandments. But love your neighbor as you love yourself; this is the greatest of them all." (Or something like that. That is pretty close to what He said.)
When He says, "Keep the Commandments," He means the Ten Commandments in the Old Testament. We are to continue to obey the laws of God in the Ten Commandments. "Love your neighbor as you love yourself," is the New Commandment given by Jesus for all of us to use as the first and greatest of all the Commandments to follow and obey, and pattern our lives by this rule. I think He also means that we keep reading and learning what the Old Testament says. All the things in that Old Testament still apply to our daily lives and how we live them.
We are commanded by Jesus to keep the old, and add the new, and form our lives from a combination of the two. I believe that is clear for all to see.
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This is a very general question. It takes books and a lot of reading.
The part about Islam is the one that I can help with.
Islam's ethical system covers everything:
war, family, investment and monetary issues, the way you treat others,....
it ranges from a smile that is considered a charity to backbiting being a terrible vice, to defending the oppressed as a great honor, and killing the peaceful being strictly prohibiting and punishable.