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.
Modern Orthodox Judaism
Nevertheless, the two movements are philosophically distinct on two broad counts.Applying the above distinction, in Israel today, Modern Orthodoxy - as distinct from (right-wing) Religious Zionism - is represented by only a select group of institutions: the Religious Kibbutz Movement, Neemanei Torah V'Avoda, the Meimad political party, and the Shalom Hartman Institute, Yeshivat Har Etzion / Migdal Oz and Yeshivat Hamivtar/Ohr Torah Stone Institutions/Midreshet Lindenbaum (some would include Yeshivat Hesder Petach Tikva, Yeshivat Ma'ale Gilboa, and the Tzohar Foundation).