Where they differ as faiths is that Judaism is waiting for the Messiah, Christianity isn't. Christianity, however, was correctly labeled a Jewish sect by Gentile historians in the 1st century. I'm not that interested in your 1) revisionism 2) disdaining my opinion as a Jew. If you're a Gentile, I'll go on a limb and say I understand what is Jewish better.
Unless you are of the few who regards Josephus mention of Christ as NOT an interpolation not a single first century historian even MENTIONS Christianity. The word doesn't show up until the second century in history.
Out on a limb may have been the right choice of words because if you understand Judaism that includes its history and the fact that Christianity is not mentioned in the first century, a Roman religion too, does nothing for your claim to understanding, how do you understand without all the facts?
You don't. I am not Jewish, I'm Muslim, but I would say that I at least have a better knowledge of first century Jewish history because I know that the second century is the first mention of Christianity or Paul in the historical records.
Iranaeus was first to mention Paul after they robbed Marcion of his creation and merged it with the religion of the real Apostles who actually knew Jesus PBUH.
Justin Martyr the first to mention Christianity as A religion, period, and it is based on Judaism but not Judaism at all.
Nazarenes were what Jewish disciples of Yesha were called and Ebionim/Ebionites, they were actually declared heretical even though it was Jesus PBUH religion.
Nazarenes aren't mentionied until Jerome and Epiphanius, 4th or 5th century, Ebionites in the second.
Apocrypha doesn't count, ie Ignatius or Polycarp, Clement of Rome or Barnabas as they can't be dated and were theological not historical. Both reasons are valid, Clement is anonymous and exists in a lone MS. in a fourth century Greek Bible with Barnabas and Hermas too.
Christianity is fully Greco-Roman, pagan, and at best pseudo-Judaic.