One of the basic beliefs of Christianity is that the Christian God is the God of Judaism, the God of Abraham and Moses. That Jesus is the Messiah that that God promised to send. If the Christian God is NOT the God of Judaism then Christianity is false.
If you are not saying that the Jews are right and the Christians are wrong you cannot say that the Jewish God is not the Christian God. Christians say He is, Jews arguably say He isn't (although even a Jew might say that Christians worship the same God but are mistaken about His nature).