What does Romans 9 teach about the distinction between Israel and true Israel?

In Romans 9, Paul clarifies that mere physical descent from Abraham does not equate to being part of God's chosen people. He makes a distinction between 'not all who are descended from Israel are Israel,' asserting that true Israelites are the ones defined by faith and election, not merely ethnicity. This teaching emphasizes the concept of the remnant, suggesting that God's grace operates through a spiritual Israel, comprising believers from both Jews and Gentiles. This underscores the principle that God's covenant community is defined by faith rather than national identity, making it vital for Christians to recognize their inclusion in the family of God through faith in Christ.