Is the Torah and the Tenakh the same thing?

No. While it is convenient to think of Torah as "the old testament", it is the the books of the instruction. Where we came from, how we are supposed to live, and where we are going is contained in Torah. The five books are Genesis, Exodus,Numbers, Leviticus, and Deuteronomy.

Tanakh is the entire "Old Testament." It includes the writings, the Torah, and the Prophets.