What is the basic difference between a Jewish person, a Catholic person, and a Christian person, they all worship the same God, but in different ways?
There are some other key differences in addition to and more specifically than those listed above.
1) Jews believe that Abraham was the last prophet sent by God, and that The Prophet will come again, but Jesus was not him. They are still waiting for the Second Coming.
2) The Jewish Bible, the Torah, is basically the first five books of the Old Testament. The parts of the Christian Bible after that are not believed in or subscribed to by Jews.
3) Jews celebrate some different religious holidays, for example, they obviously do not celebrate Christmas or Easter, but they do observe the Passover as Christians do.
4) Catholics also believe very strongly in the idea of absolution of sin. That those who confess their sins can be forgiven by God through a Priest on Earth. The Catholic Church is much older, and has a single religious leader, the Pope, while other Christian denominations like Lutherans and Baptists do not. Catholics also believe in sainthood. Catholicism is one sect of Christian religions.
Actions are very important to Jewish people. Roman Catholics and other denominations believe that beliefs in God are more important. Another difference is that Jewish people have no official creed unlike Roman Catholics, etc.
Jewish people also read the Torah, not the Bible. This is one of main differences in religions.
Jewish people also do not believe that Jesus is the Messiah but ALL Christians do. Jewish people have expectations of what the Messiah was supposed to do and they feel that Jesus did not fulfill these expectations.
They do worship the same God but in different ways. Roman Catholics have a set of beliefs (creeds or doctrines) in place and they also believe in communion, or the taking in the body (bread) and blood (wine) of Christ. Some other Christian denominations do this but not all.
Just to give you a quick kind of summary to answer your question:
Jews believe in the same God as Christians, but they do not believe that Jesus was the son of God. They believe in God, but not Jesus, to put it simplistically.
Christians believe in the same God as the Jews, but they also believe that God sent his son, Jesus, to live on earth as a prophet and Messiah.
Catholics are Christians. Catholics are one denomination out of many denominations of Christians. But in terms of what makes Catholics different from Jews, there aren't any major differences between Catholics and other Christian denominations.