Christians: Why do some think all Israylites are Jews and all Jews are Israylites WHEN...?

Excellent Question! There is a distinction between two main branches of Israylites. House of Israyl and House of Judah. Many misunderstand the term 'jew' would apply to House of Judah at best and the House of Israyl is not spoken of that way in the entire bible. One of the above responders claims the House of Israyl ws taken into Babylonian captivity. This is not true at all. The House of Israyl had gone into yrian captivity roughly 125 years before the Babylonian captivity and many of those in the House of Judah had been taken at that time as well. The rest of House of Judah many years later are taken in the Babylonian captivity and maintain the title 'jew', though this can mean many things today instead of someone that is actually part of physical stock children of Jacob. Interestingly these of the House of Israyl are referred to the NT writings many times as 'gentiles' because they had been 'put away' and become 'not a people' and Hosea says. But he goes on to say how they would become His people once again, and this is who gets 'adopted' into the faith. Rom.9:3-5.