Judaism is a religion based on the history of the Tanach, updated and analyzed by rabbis throughout history since the return of the Jews from the Babylonian exile. Mostly renovated by rabbis of the Pharisaical class, the system presented in the Torah was reworked to move the focus from the temple, controlled by the Sadducees and rapidly being corrupted, to home and synagogue worship. In doing so, the Pharisees implemented fundamental changes to Mosaic Law, such as the complete erasure of the high priesthood, and the destruction of the sacrificial system.
The current practice of the Jewish orthodoxy is correctly labeled as Judaism, and is based on the Talmud, an attempt at exegesis of the Tanach by many rabbi. It is the way Jewish teachers applied Scripture to daily life, seeking to make the Tanach not only applicable, as it was (and is still) believed it already was, but clear and precise in every event in routine life. However, with the corruption of the high priesthood in the last years of the Jewish nation before its destruction in 70 A.D., and the consequent collapse of the entire formalized system of Mosaism, many of the interpretations reflect a de-centering of God's (YHWH, Yahweh, Jehovah) presence in the the temple, and not just a downplay but total revisal of the meaning of sacrifices.