Israelite – Any descendant of Jacob.
Israelite, or of Israel, requires a blood-linage to one of the 12 tribes of Israel (Romans 11:1), which is identified by circumcision (Acts 7:8, John 7:22).
Israelite is a generic term of nationality, without any connotation of religious service or faithfulness to God; it is simply a statement that they belong to the nation who inherits the promise of God through Jacob; a statement of birthright.
A gentile could be born or bought into the nation of Israel, but though they were required to live like an Israelite, they could never become a child of promise … they have no inheritance.
The false teaching today, in Christianity, is that gentiles are ‘spiritual Israelites’ or ‘spiritual Jews’. Therefore, since Israel has been diminished during the Dispensation of Grace (Romans 11:11-12), the Christians now own Israel’s promises. That teaching is a lie.
God said that Israel will be his chosen people until the entire solar system ceases to exist (Jeremiah 31:35-37). The promises that God gave to Israel belong to Israel, and Israel only.
This issue was discussed completely in “The Truth According to Scripture; Book One; Basic Bible Knowledge”, which is available on Amazon. You can also get a FREE PDF version.
See also Christian, Gentile, Grecian, Heathen, Jew, Proselyte