Not true. The terms Jew and Israelite became synonymous terms from about the time of the Captivity in Babylon (586 B.C.).
Lets see what Paul calls himself in Romans 11:1
I ask then: Did God reject his people? By no means! I am an Israelite myself, a descendant of Abraham, from the tribe of Benjamin.
Paul answered, “I am a Jew, from Tarsus in Cilicia, a citizen of no ordinary city. Please let me speak to the people.”
Then Paul said: "I am a Jew, born in Tarsus of Cilicia, but brought up in this city. Under Gamaliel I was thoroughly trained in the law of our fathers and was just as zealous for God as any of you are today.
From the time of the return of the first remnant after the Babylonian exile, sacred historians, prophets, apostles, and the Lord Himself, regarded the “Jews” whether in the land or in “Dispersion” as representatives of “all Israel,” and the only people in line of the covenants and the promises which God made with the fathers (see the following passages where the use of Judah and Israel are found interchangeably: Zechariah 1:19; 8:13 10:6 Ezra 6:17; 8:35, etc.).