Judaism and Christianity are in many ways different and in many ways similar. While Christians believe that people will receive judgment after death, going to either heaven or hell based upon whether they have accepted Jesus Christ as their savior, Jewish people are not unified on the subject. Some believe in a form of reincarnation. Others believe that people will be in some way united with God.
Christianity has a number of rules depending upon the denomination. The rules are those found in the Old Testament and those drawn both from Paul’s writings and the gospels in the New Testament. Generally speaking, people are expected to love their neighbor and put God first, though there are myriad other rules, too. In Judaism, the rules are more distinct. The Talmud provides a number of practical rules for living, including rules on how to dress, what to eat, when to worship, and the like.
Depending upon the denomination, Christian churches are led by priests, bishops, pastors, or elders. The power structure can be very different from church to church. In modern Judaism, rabbis are at the head of synagogues. Scribes, cantors, and mohels are also among the leaders of the Jewish church.
Sin is the central concept in Christianity. People are said to be flawed sinners, which is why they need to seek salvation from their sin from Jesus. In Judaism, action is more important than belief. People are required to do more than just confess their sin. They are asked, and in fact required, to go and seek forgiveness from the person that they have sinned against.
Membership in Christianity mostly comes through conversion. People can choose to believe in the religion and be baptized. Judaism gets most of its adherents from heredity. People are born Jewish in a cultural sense, though there are some people who convert to the religion.