So the Assyrians (in the part of the world that is now south Turkey and Northern Iraq) conquered Samaria. The Babylonians (in the part of the world that is now southern Iraq) later conquered Judah. Then Cyrus of Persia conquered Babylon and allowed the Jews to return to Persia. Which Jews? The exiles from Samaria, the exiles from Judah (assuming there were exiles from Juday), or both? What happened to the Assyrians? Did Cyrus, by conquering Bablyon, also assimilate in one fell swoop the old Assyrian empire?
Related question - What happened to the Assyrian empire between its conquest of Samaria and the advent of King Cyrus?
More on this in the coming Staf Reports on the composition of the Bible. It’s hard to give a “little” background. The northern tribes disappeared, as covered by an earlier staff report: What’s up with the ten lost tribes of Israel?
The southern tribes were taken in captivity to Babylonia, and the remnant of those tribes are the ones who were allowed to return to Judah under Cyrus. Somewhere around there, they were called Judeans or Jews rather than Israelites. That help?
On the history of Assyria, Babylonia, Persia, and so forth, I suggest any World History (Ancient) text book to set you aright.