Both Torah and the Old Testament relate to Jews. How different or similar is Torah and the Old Testament of Bible?
I've found "Judaism 101" at jewfaq.org to be a reasonably sound site when looking for answers to questions about Judaism. Here's their basic definition of Torah:
The word "Torah" is a tricky one, because it can mean different things in different contexts. In its most limited sense, "Torah" refers to the Five Books of Moses: Genesis, Exodus, Leviticus, Numbers and Deuteronomy. But the word "torah" can also be used to refer to the entire Jewish bible (the body of scripture known to non-Jews as the Old Testament and to Jews as the Tanakh or Written Torah), or in its broadest sense, to the whole body of Jewish law and teachings.
In everyday usage, speakers commonly use the word "Torah" as a synonym for what Christians sometimes call the Book of Moses.
Worth noting is the fact that the Torah is one of many central texts used in Judaism -- the Talmud, Mishnah, and other texts are also significantly important. Book one of Edersheim's The Life and Times of Jesus the Messiah explores the topic in significant depth.
List of books accepted by Jews and Christians are almost similar with some little differences. Canonization may be different but the individual books are same, only the list is different.
In short, Torah and Old Testament is relatively the same. It's all about the Jews and their history. For the Jews, it is their history and the Laws given to them by God. For the Christians, it is a shadow of the New Testament which fulfills its prophecies regarding the Messiah and many others.
First of all: what is in Torah are the teachings of God to Israel. Torah today contains these teachings. There are no Torah scrolls older than the 10th. cent. Most of Torah is oral teaching, which was passed down orally until the 3rd. cent A.D. when the oral Torah was finally written down.
The Church in the 3rd. century were pressured to include the OT as part of the Bible, in order to counter the arguments of Gnostic religions. The Church scholars, who were Greek at that time, could not refer to the Hebrew writings because Hebrew scholars in the Church had left the Church.
The Church wrote the "Old Testament" - the version that is in most English Bibles - from a 3rd. cent. B.C. Greek document called the Septuagint, which was a translation of Jewish documents with a few Greek additional books thrown in (actually they used Origen's Greek version in his Hexapla which included three Greek versions including Septuagint.) Septuagint was universally condemned by the Judean authorities, and it was forbidden to even study Greek in Jerusalem. Later in the 5th. cent, the Church revised the Old Latin translation of the Greek Septuagint using Hebrew writings translated into classical Latin by Jerome. This version of the OT is currently part of the Latin Vulgate Bible which was translated by Cambridge scholars into English in the 16th. cent. (the Duoay-Rheims Bible.)
To see the differences between a Christian OT and Torah, you must read a Jewish "bible" - The Chumash Stone Edition, or the Etz Hayim, for examples. These are five times thicker than the Pentateuch in the English Bible, as they contain both Written and Oral Torah, which are equally sacred.