It all depends on what time period/era we are talking about.

The original split was the Tribe of Judah with the Tribe of Benjamin breaking away from their Israelite cousins.

Later, as you pointed out, some Levites and others also left the Kingdom of Israel and moved to the Kingdom of Judah. All of these people were Israelites, as they were direct genetic descendents of Jacob/Israel and his 12 sons.

But once the Babylonians captured them and took them off to Babylon, it all changed.

When they came back, the people living in the former Kingdom of Judah were a variety of people. Some were original Judahites and other Israelites.

But other people were Edomites (jews), Canaanites (jews), Hittites and others.

By the time of Jesus, the area was under the control of the Roman Empire, and that area was now a province of Rome called Judea.

The Bible, especially the New Testament, cannot really be understood without understanding this history.

That's because the word "jew" was never in the original text in Hebrew or Greek.

It was an English word that was created more than 1,000 years later to describe certain people who (a) were resident in the Roman province of Judea (and thus, "Judeans"), (b) were not genetic descendents of Jacob/Israel (thus were not "Israelites" nor "Judahites"), but (c) pretended that they were.

Also, they practiced Judaism, not Hebrewism (pre-Christianity).

This is why Jesus talks to them and refers to them the way He does in John 8 and Rev 2 & 3.

It all depends on what time period/era we are talking about.

The original split was the Tribe of Judah with the Tribe of Benjamin breaking away from their Israelite cousins.

Later, as you pointed out, some Levites and others also left the Kingdom of Israel and moved to the Kingdom of Judah. All of these people were Israelites, as they were direct genetic descendents of Jacob/Israel and his 12 sons.

But once the Babylonians captured them and took them off to Babylon, it all changed.

When they came back, the people living in the former Kingdom of Judah were a variety of people. Some were original Judahites and other Israelites.

But other people were Edomites (jews), Canaanites (jews), Hittites and others.

By the time of Jesus, the area was under the control of the Roman Empire, and that area was now a province of Rome called Judea.

The Bible, especially the New Testament, cannot really be understood without understanding this history.

That's because the word "jew" was never in the original text in Hebrew or Greek.

It was an English word that was created more than 1,000 years later to describe certain people who (a) were resident in the Roman province of Judea (and thus, "Judeans"), (b) were not genetic descendents of Jacob/Israel (thus were not "Israelites" nor "Judahites"), but (c) pretended that they were.

This is why Jesus talks to them and refers to them the way He does in John 8 and Rev 2 & 3.