In Romans 9:4 Paul tells us who he means when he uses the word "Israel". He defines the word "Israel" for all of us. Jewish believers in the Church generally always kept their own identity and tended to more deeply revere the words of their fathers on their side of the Book, but they were still Christians.
The Gentiles and the Jews shared the same faith in their father Abraham but different promises, the one to be blessed with the gift of salvation along with the other, but Jewish believers were also to inherit the Land of Israel as the Abrahamic Covenant clearly promised.
Analogies seldom work properly. When my wife married me she did not become me but she legally became my heir to all that I own. Likewise, if I were to divorce someone they no longer have claim to my estate.
There are no different promises; one to the Jews and one to the Gentiles. We share the same promises because we are ONE in Christ; both Jews and Gentiles. God doesn't look down favorably on unbelievers who have rejected His Son.