Is it the same God?

Q: Is it the same God?

Would you say Christians worship the same God as Jews, and Muslims?
If no, why?
I think it’s all the same God, just different ways to worship.
This is not a question of who is right or wrong.

A: From the official Catechism of the Catholic Church:

The Church and non-Christians

839 “Those who have not yet received the Gospel are related to the People of God in various ways.”325

The relationship of the Church with the Jewish People. When she delves into her own mystery, the Church, the People of God in the New Covenant, discovers her link with the Jewish People,326 “the first to hear the Word of God.”327 The Jewish faith, unlike other non-Christian religions, is already a response to God’s revelation in the Old Covenant. To the Jews “belong the sonship, the glory, the covenants, the giving of the law, the worship, and the promises; to them belong the patriarchs, and of their race, according to the flesh, is the Christ”,328 “for the gifts and the call of God are irrevocable.”329

840 And when one considers the future, God’s People of the Old Covenant and the new People of God tend towards similar goals: expectation of the coming (or the return) of the Messiah. But one awaits the return of the Messiah who died and rose from the dead and is recognized as Lord and Son of God; the other awaits the coming of a Messiah, whose features remain hidden till the end of time; and the latter waiting is accompanied by the drama of not knowing or of misunderstanding Christ Jesus.

841 The Church’s relationship with the Muslims. “The plan of salvation also includes those who acknowledge the Creator, in the first place amongst whom are the Muslims; these profess to hold the faith of Abraham, and together with us they adore the one, merciful God, mankind’s judge on the last day.”330

842 The Church’s bond with non-Christian religions is in the first place the common origin and end of the human race:

All nations form but one community. This is so because all stem from the one stock which God created to people the entire earth, and also because all share a common destiny, namely God. His providence, evident goodness, and saving designs extend to all against the day when the elect are gathered together in the holy city. . .331