Judaism
Christianity was originally a sect of Second Temple Judaism, but the two religions diverged in the first century. The differences between Christianity and Judaism originally centered on whether Jesus was the Jewish Messiah but eventually became irreconcilable. Major differences between the two faiths include the nature of the Messiah, of atonement and sin, the status of God's commandments to Israel, and perhaps most significantly of the nature of God himself. Due to these differences, Judaism traditionally regards Christianity as Shituf or worship of the God of Israel which is not monotheistic. Christianity has traditionally regarded Judaism as obsolete with the invention of Christianity and Jews as a people replaced by the Church, though a Christian belief in dual-covenant theology emerged as a phenomenon following Christian reflection on how their theology influenced the Nazi Holocaust.
Judaism
Like the Sadducees who relied only on the Torah, some Jews in the 8th and 9th centuries rejected the authority and divine inspiration of the oral law as recorded in the Mishnah (and developed by later rabbis in the two Talmuds), relying instead only upon the Tanakh. These included the Isunians, the Yudganites, the Malikites, and others. They soon developed oral traditions of their own, which differed from the rabbinic traditions, and eventually formed the Karaite sect. Karaites exist in small numbers today, mostly living in Israel. Rabbinical and Karaite Jews each hold that the others are Jews, but that the other faith is erroneous.