I have 3 questions about these:
How are these different, and how are they similar?
Are they all Jewish books?
How did they come about?
Torah can mean several things:
Most basically it means the divinely revealed teaching (usually translated 'Law" by Christians, but the Jewish rabbi I know best strongly dislikes that translation) that governs the lives of Jews. This teaching is found in its most authoritative form in the “Five Books of Moses,” which Orthodox Jews believe were essentially dictated to Moses by God at Mount Sinai. Therefore, these books are often referred to as Torah.
However, Orthodox Jews believe that there is also an “oral Torah” which was revealed by God to Moses at Sinai but not written down for centuries later. (Conservative Jews are more open to the view that this content is of later origin altogether, I believe.) Eventually, much of this oral Torah was written down in a document called the “Mishnah,” which records the judgments of various rabbis concerning questions of Torah. The rabbis recorded in the Mishnah lived more or less during the couple centuries surrounding the lifetime of Jesus (up to the early second century of our era), and the Mishnah itself was written down probably around A.D. 200. Over the next few centuries, other rabbis commented on the Mishnah and gave further elaboration of the oral Torah, and this commentary was added to the Mishnah to create the Talmud. (There are actually two Talmuds, but the more important one is the “Babylonian Talmud” written down around the sixth century).
At the same time, many rabbis were having mystical experiences and writing about them. This mystical tradition shows up occasionally in the Talmud, but much of it wasn’t included there. In the Middle Ages, mysticism became more important, and Jewish mystics claimed that their teachings had been handed down by tradition from the ancient rabbis. The word “Kabbalah” basically means “tradition.” The most important document of the Kabbalah is the Zohar, which was probably written around the 13th century but claims to record the teachings of the ancient Talmudic rabbis.
I hope this is somewhat helpful. You have asked a complex set of questions. One of the best and clearest websites dealing with these matters is
www.jewfaq.org. The author of the website seems very well informed, although she is not a rabbi or a professional scholar as far as I can tell. Generally I have found that what she says checks out with other, more authoritative sources.
Edwin