While Christianity can be said to stem from Judaism, since the primary religious figure, Jesus Christ, was a Jew, there are a few key differences between the two. Most importantly is the role of Jesus Christ himself. Christians believe that Jesus is the son of God, the savior prophesied to save the world from its sins. Jews, however, do not believe that Jesus is this savior, as their understanding of the prophecy was that the savior would be a warrior who would lead them to the promised land. As such, Jesus does not play a strong role in the Jewish theology, and any holy days associated with Jesus (Christmas, Easter, Advent, Lent, and several other Catholic holy days of obligation) do not exist in the Jewish calendar.
Furthermore, the central religious texts belonging to the two faiths differ in that the Christian Bible is significantly longer than the Jewish Torah. In fact, the first five books of the Christian Bible, Genesis, Exodus, Leviticus, Numbers, and Deuteronomy (known as the Pentateuch), are in fact the Jewish Torah. However, the first half of the Christian Bible, the Old Testament, also plays a part as a religious text in the Jewish faith. The main difference is the fact that the New Testament, the latter half of the Christian Bible, is not considered a religious text in the Jewish faith, as it follows the life of Jesus Christ. For a more extensive and theological explanation of the differences between the Bible and the Torah, check the first link below.
Beyond these more theological differences, the Jewish and Christian traditions can be very different. In the Jewish tradition, the transition into adulthood is celebrated at thirteen by a Bar Mitzvah for boys and at twelve by a Bat Mitzvah for girls. In the Christian tradition, the Holy Sacrament of Confirmation is a similar celebration; however, it does not necessarily mark entrance into adulthood, but rather full membership within the Church, and is done at different ages depending on the branch of Christianity. Another difference occurs in traditions regarding death and burial. While expediency with regards to the internment of the body, as well as care that the body is intact, are crucial to the Jewish faith, Christians do not have any rules regarding how soon the body is to be buried. Furthermore, while Christians have a particular format for the funeral service (Catholics especially), Jews have a much more prescribed set of rituals to be followed to ensure the soul can return to its Source, which include the Taharah, in which the body is ritually cleansed, and Levayah, which is the funerary service. For more in-depth descriptions regarding the various traditions, follow the second link below for Christian traditions and the third link for Jewish traditions.