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.