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.
Jews
After the destruction of the Second Temple, Judaism lost much of its sectarian nature. Nevertheless, a significant Hellenized Diaspora remained, centered in Alexandria, at the time the largest urban Jewish community in the world. Hellenism was a force not just in the Diaspora but also in the Land of Israel over a long period of time. Generally, scholars view Rabbinic Judaism as having been meaningfully influenced by Hellenism.