As I see it, the basic difference between Judaism and Christianity is that, at least at one time, the Jews were looking for the Anointed One to come (I'm not sure what modern Judaism is looking for). Christians believed that the Anointed One has come, fulfilled the Law, thereby establishing the New Covenant prophesied by Jeremiah.
If you want to better understand the differences, please read Romans or Hebrews, written in the First Century AD.