It's my understanding that Mitzvah (Mitzvot -pl.) translates to commands, or deeds, and Torah is the Law a whole. Also it is the first 5 books of the Bible: Genesis, Exodus, Leviticus, Numbers, Deuteronomy.
Mitzvah - There are 613 total mitzvah in scripture. There are 248 positive (as in, do this) and 365 negative (as in, don't do this).
ex: "You are to have no other gods before me," (Exodus 20:3)
"You are not to make for yourselves a carved image or any kind of representation of anything in heaven above, on the earth beneath or in the water below the shoreline," (Exodus 20:4). Torah - The Law (first 5 books of the Bible). But, the Torah can also refer to the entire Jewish scriptures, the whole "Old Testament," (The Law, The Prophets, and The Writings). Scripture verses including "mitzvah" and "Torah" together
- Joshua 22:5 - "Only take great care to obey the mitzvah and the Torah which Moshe the servant of ADONAI gave you - to love ADONAI your God, follow all his ways, observe his mitzvot, cling to him, and serve him with all your heart and being."
- Proverbs 6:23 - For the mitzvah is a lamp, Torah is light, and reproofs that discipline are the way to life. - Mark 12:28-31 - "One of the Torah-teachers came up and heard them engaged in this discussion. Seeing that Yeshua answered them well, he asked him, "Which is the most important mitzvah of them all?" 29 Yeshua answered, "The most important is, `Sh'ma Yisra'el, ADONAI Eloheinu, ADONAI echad [Hear, O Isra'el, the LORD our God, the LORD is one], 30 and you are to love ADONAI your God with all your heart, with all your soul, with all your understanding and with all your strength.' 31 The second is this: `You are to love your neighbor as yourself.' There is no other mitzvah greater than these." http://www.jewfaq.org/613.htm http://www.jewfaq.org/torah.htm