Thanks so much for asking this, Avis! So first, to make things nice and confusing, Jewish people are an ethno-religion, which means they are both a race and a religion (I wrote about this a little bit in my newsletter from last week). The vast majority of Jews are indeed descendants of the Hebrews in the bible; Judaism is not a proselytizing religion (in fact it's notoriously very difficult to convert because the tradition is historically extremely insular), which is part of why the population is so small--only 17.8 million Jews in the world, less than .2% of the world's population. Jews were forced out of Israel after living there for thousands of years (which is corroborated by archaeology and genetics) through several waves of invasion and corresponding diaspora (invaded most prominently by Romans and later Arab conquests), though a small number of Jews managed to remain in Israel. Jews fled to different countries throughout Europe, the Middle East and Northern Africa (although, Black Ethiopian Jews are pre-diasporic; meaning, their distinct Jewish genealogy, which allegedly dates back to the lineage of Moses himself, reaffirms part of modern Ethiopia as one of the ancient 12 Tribes or Kingdoms of Israel).
As Jewish refugees have become increasingly unsafe in an increasingly globalized world (expelled from dozens of countries, slaughtered in events like the Holocaust or the Spanish Inquisition, wiped out in places like Iran and Morocco and Yemen, etc or tortured and oppressed in things like the Pogroms in Russia), assimilation has become increasingly favorable for many Jews. The result is more and more interfaith marriage (which may or may not mean that one's spouse would convert to Judaism and/or the Jewish person might shed their religious identity), and a lot more ethnically Jewish atheists, or Jews who may identify as "culturally" Jewish but not religiously. The fact of the matter is, however, an ethnically Jewish person will maintain distinctly Jewish DNA regardless of the status of their cultural identity or practice. And the DNA of Jews across the world, whether they are Sephardic, Beta Israel, Ashkenazi or Mizrahi has distinct shared commonalities. Incidentally, even the light-skinned Jews who may have been living in America for generations after escaping from somewhere like Russia, still have closer DNA to other Middle-Eastern people like Palestinians who have been living continuously in that region since the Jewish diaspora (and there may or may not have been some intermarriage between Jews and Palestinians by the time Palestinians were recorded to have arrived, allegedly around the 7th century, though it may not be entirely likely since again, Jewish communities have historically been incredibly insular).
So to answer your question about whether to say "Jews" or "the Jews," I would recommend just using discernment. Like I said, if you're following the phrase with a generalization or something pejorative, best not to say it. But if it's part of a respectful discussion that is not vilifying, I think it's generally fine. I would just try to be aware of tone and make sure that there isn't an angry or resentful or accusatory tone when you refer to "Jews" or "the Jews," but if you're at all concerned or unsure, then you can always just defer to saying "Jewish people." Let me know if you need any clarification and again thank you for asking this question! I know it's confusing and weirdly not commonly covered or understood so I appreciate it.
