To answer the question whether they worship the same God, it is
best to express mathematically, ie. Jews say 'same' for the
Christian God and Christians say 'same' for the Jewish God.
Do the Jews believe in the Trinity? No. When the Church was at its
infancy, people were struggling with the nature of God, most often
with the nature of Jesus. This understanding is very important. You
can't sui2 sui2 bian4 bian4 say you share the same God if your
understanding is off.
"One God, alone unbegotten, alone everlasting, alone unbegun, alone
true, alone having immortality, alone wise, alone good, alone
sovereign." Monotheistic God. Follows the Great Shema of Israel
also. Sounds pro huh? Sorry, but this is Arianism. May I remind
everyone this is a heresy.
On the other hand, Christians can say they share the OT God with
the Jews. But cut the crap lah. This affirmation is no more than a
polite gesture to make the Christian God more encompassing and less
exclusive. The fact is, if you're trying to understand God purely
from the OT, you're most likely gonna to arrive at a heresy, like
Arianism above. Christians have the benefit of the NT, that's why
they can make such statement. Thus such statement is not entirely
fair.
May I remind everyone salvation comes from believing Jesus Christ
died for your sins. This is the cornerstone of Christianity. God
didn't die in the OT.