There is spiritual Israel, and there is natural Israel. Natural Israel are all those who are descendants of Abraham by the flesh. Spiritual Israel are all those who have the faith of Abraham who look forward to the day of Christ. Because of the faith of Abraham, GOD counted it to him for righteousness, Genesis 15:6 & Romans 4:3. Spiritual Israel are those who believe in the atoning sacrifice of Christ at the cross of Calvary.
Just as Abraham believed that GOD would have resurrected Isaac from the dead when GOD told him to sacrifice him, this was symbolic of Christ's own sacrifice. Isaac was the son of promise to Abraham, not Ishmael. Isaac's son was Jacob who the Lord changed his name to Israel who is the father of the twelve patriarchs, who were the fathers of the nation of Israel. Their descendants are the Israelites now called in present day, Israeli's. Romans 4:13 says of the gentiles, " For the promise that he should be the heir of the world, was not to Abraham, or his seed (natural descendants), through the law, but through the righteousness of faith."
Hebrews 11:17-19 says, (17) By faith, Abraham, when he was tried, offered up Isaac: and he that had received the promises offered up his only begotten son, (18) Of whom it was said, That in Isaac shall thy seed be called: (19) Accounting that GOD was able to raise him up, even from the dead; from whence also he received him in a figure.
This is further confirmed in Paul's letter to the Galatians. In chapter 3 he says, " O foolish Galatians, who hath bewitched you, that ye should not obey the truth, before whose eyes Jesus Christ hath been evidently set forth, crucified among you?"
Verses 6 & 7 says, (6)"Even as Abraham believed GOD, and it was accounted to him for righteousness. (7) Know ye therefore that they which are of faith, the same are the children of Abraham."
Thus, we who believe that Christ died to redeem us from the degradation of sin are Israel.