Yes. There is the earthly city of Jerusalem and the heavenly city called "New Jerusalem." Two distinct descriptions. One ungodly, the second godly.
That is the same as descriptions of Israel. Those cast off by God for unfaithfullness are the earthly, ungodly Israel. Those called to faith and salvation by the grace of God, are the redeemed and godly Israel.
Same thing with God's Covenant with mankind. The first (old) Covenant was one of works which does not save, and the second (New) is the Covenant of Grace that gives everlasting life to all the faithful and elect church body of Jesus Christ; Jew & Gentile.
There is one national Israel, but four definitions of "Israel." l. God's Son is named "Israel." Hosea 11:1, Matthew 2:15 2. The northern tribes of Israel were distinct from the tribes of Judah. 3. The ungodly citizens of Israel are distinguished from the remnant of faithful souls saved out of the nation. 4. Israel is the spiritual body of believers who abide by faith in Jesus Christ; the church of God; the New Jerusalem.
Galatians 4:21-31 reveals these descriptions and distinctions of the significance of Israel in the purposes of God.
God's enemies are not beloved. Ungodly souls are reprobate. Only the Elect in Christ are beloved by God, through Him.
Agreed. Many, but not all . . .
Agreed. MANY, but not all . . .
Exactly.
The Jewish election was temporal and national. Out of all the nations, the Jews were chosen by God to represent the Covenant promises of a Saviour. They were not elect unto salvation, for most of the nation of Jews proved to be reprobate and unfaithful to God, for they did not believe His promises. The nation of Israel suffered because of their sins and unbelief, not because they were elected to handle the holy ordinances amongst all the nations.
None of the remnant of Jews, saved by the grace of God, were cast away or rejected. They were reconciled to God according to election unto everlasting life, and gifted with belief in the promises of the Saviour. Romans 11:4-8