Because the Bible labels Abraham as the first Hebrew (Genesis 14:13) and because Jacob, Abraham’s grandson, had his named changed by God to Israel (Genesis 35: 10), all descendants of Abraham, Isaac (Abraham’s son), and Jacob can be called Hebrew Israelites.
Often we view the whole of Hebrew Israelites as Jews, but technically speaking, they aren’t. That’s because the ancient nation of Israel was split into north and south kingdoms after the reign of King Solomon. In the Northern Kingdom, resided the, let’s say, “non-Jewish” Hebrew Israelites. They are the direct descendants of ten of Jacob’s sons.
Those in the Southern Kingdom were direct descendants of Jacob’s other two sons. One of those sons was named Judah. The region in which he lived was called Judea, and the people there were called “Judahites” or “Judeans.” Later, Judeans were simply identified as “Jews.” So, again, technically speaking, a true biblical Jewish person is a reference to a Hebrew Israelite from the region of Judea.
However, of course, things changed through the course of mixed marriages, migration, religion, politics and a desire to be unified. As a result, modern-day Israel established itself as a Jewish nation. It defines itself that way in The Basic laws of Israel, a part of its constitution.
A person in Israel is now considered to be Jewish under three circumstances: (1) those born into a Jewish family regardless of whether or not they practice Judaism; (2) those who are of some Jewish lineage or ancestral background; and (3) those without any Jewish lineage or background, but who have converted to and are practitioners of Judaism.