What are some of the main differences between the Jewish celebration of Passover from the Christian celebration of Easter?
They are quite unlike each other. You can read of the fundamentals of the Jewish Passover in Exodus 12. In fundamentalist Christianity, Easter is the celebration of Jesus' resurrection from the dead. You can read of the resurrection benefits for the Christian in 1 Corinthians 15. Wikipedia should have articles on each if you want to be more thorough. I will give an summary of these.
In the Jewish Passover, the Jewish people celebrate the time when their forefathers were slaves in Egypt and God spared them from death and brought them out of Egypt. He had first told the Jews (in Exodus 12) what to do to make sure they were not included in the judgment, including killing a lamb and dabbing blood around the door. When the avenging angel went from house to house to kill the firstborn throughout Egypt, and God saw the blood, He "passed over" that house, keeping the angel from entering in.
The secular version of Easter is as a harmless holiday. Easter began as a pagan religion to Astart the goddess of fertility - that's why symbols such as rabbits and eggs are incorporated into the holiday, and it takes place in the spring when new life begins after a cold winter.
The Christians have taken the holiday to celebrate the resurrection of Jesus from the dead. (New life - get it?) The eggs and rabbits usually don't enter into it except sometimes as holiday fun.
Your confusion may be because at one point in the biblical narrative, Jesus celebrates the Passover with His disciples (see Matthew 26). There, He applied the blood to Himself. In later books in the New Testament this is expanded: He was God's lamb to be sacrificed in their place so they would be set free from slavery to sin. Christians continue to do this "Lord's Supper" or communion with bread and wine, sometimes weekly, sometimes more or less often, and often on a Sunday. This Passover supper and Easter fall on the same day, and is an interesting dovetailing of the Old and New Testaments, where the OT figure of Christ (the Passover lamb) has been fulfilled in the NT.