I'm pretty sure they aren't completely not the same people either. There is the theory that the Judeans, long after the diaspora, were infiltrated by the Khazarians. My research suggests the Khazarians are nothing more than the Scythians (I'm about 99.999% sure of that). The problem people have putting this together, is that the Scythians were largely wiped out of history. People today (where by "people" I mean those who research the past, not everyone else who are completely clueless about all of this) mislabel the Scythians as the Tartarians, and there is all sorts of disinformation surrounding the Tartarians which keeps people from understanding the connection to the Scythians. See Sir Walter Raleigh, 1560, p 247 e.g. where he clearly states that the Tartarians are the Scythians. There are many other sources (all prior to the 20th century) that name the Tartarians clearly as the Scythians (see Petes, 1722, p 15 e.g.).

The Tartarians are the Scythians. The Khazarians are the Scythians. But the Khazarians aren't necessarily the Tartarians. The Scythian Empire, according to my research, controlled about 25% of the world, for between 3000-8000 years, finally dying completely in the early 20th Century (although not really, because the USSR was sorta a continuation of it). I can substantially support 3000 years, but there is up to 8000 years of a continuity of culture and language in the archeological evidence. The reason the Scythians are so easy to hide, is because they were a multi-cultural, multi-ethnic, and multi-religion Empire. Everything that says "Khanate" on any old map is just a principality of the Empire of Scythia.

The Tartarians, were, I think, what we today call the Mongolians. A subgroup of the Scythian Empire. The Empire of Scythia was a "You Keep What You Kill" type of government. In other words, the strongest clan ruled. During the time of the "Mongolian" (Tartarian) invasion, they first consolidated rule in greater Scythia, and then invaded the rest of the Eurasian continent. But consolidating rule in greater Scythia was pretty much the same thing as saying "Election Year." It happened all the time. Everyone was always paying tribute to someone. Old works talk about various Khan's bragging about how many principalities were paying them tribute. It was just how their culture worked. They intermixxed all the time as well, keeping a continuity of culture across a huge area, just like how we do it today in the United States. Many subcultures, but one overarching culture because of a single government and open borders.

The Mongolian invasion was not the first time the Scythian's all banded together and took over all of Eurasia. Another simple example is Attila the Hun. There were many others. They seemed to have some version of it about once every couple hundred years or so. Some more successful than others.

The region we now call Israel was taken as a Scythian tributary (principality) numerous times in history. But the Scythians also lost it as a principality many times, just like they lost Iraq (Assyria, etc.) as a tributary many times, and retook it many times.

The evidence suggests every single one of those regions began as a Scythian outpost. The Scythians themselves were the progenitors of the Judeans and the Assyrians/Babylonians/Sumerians, etc.. For reference, the Bible calls the Scythians the Magogians (Gog and Magog).

There are many works that suggest that Judaism is originally the worshiping of Moloch/Ba'al, etc., prior to encountering Zoroastrianism, at which time they melded their pantheon into YHWH.

The Khazarians' influx into the larger Judean community was quite a while (2000ish years) after the change of "Judaism" to monotheism. After the original Israeli diaspora (not the Judean diaspora a couple hundred years later) I think some of those who followed the previous religion we think of as Babylonian went into the area now called Khazakstan and became the Khazarians. They did so because flowing freely between Scythian states was totally a thing. I think the Khazarians melded into the present day Judeans because of their shared ancestry and similarity of the origin of the religion.