What is a Jew?
A Jew is a descendent of one of the 3 tribes of Israel which made up the Southern Kingdom.
The Southern Kingdom of Israel was comprised of the Tribes of Judah, Benjamin and Levi. It was also known as the Kingdom of Judah or House of Judah. The remaining 10 tribes made up the larger Northern Kingdom. Before they split, the combined Kingdoms were called The House of Israel. After they split, the name House of Israel went exclusively to the Northern Kingdom.
The Southern Kingdom Israelites were known as Judeans after the province of Judea which was their home. Judea in turn was named for Judah, one of the 12 sons of Jacob/Israel.
In 587 BC the Southern Kingdom was taken captive by the Babylonians, and those Israelites were taken to Babylon and held for 70 years. Only ~50,000 Judeans returned to Palestine at the end of their captivity. Some remained behind in Babylon, and others settled elsewhere.
These post-captivity Southern Kingdom refugees and their offspring were nick-named "Jews", for the Judean province which was their home. Other Judeans who eluded the captivity also shared the name. Northern Kingdom Israelites were not called Jews.
One Jewish writer opined there are at least 3 broad categories of Jews today, and his analysis went something like this: (Many may fit into more than one overlapping category.)
GENETIC Jews: Hereditary Jews are descended from one of the 3 Israelite tribes which made up the Southern Kingdom of Israel living in Judea after the split of the Davidic Kingdom. The largest was the Tribe of Judah, named after Judah who was one of 12 sons of Israel, and their Judean home was called The Kingdom of Judah. When these "Judeans" were taken into Babylonian exile about 575 BC they were colloquially referred to by their captors as "Jews", the first time the word Jew is found.
RELIGIOUS Jews:
Type (1) A small group of "Orthodox Jews" who rigorously follow the religious precepts handed down from the earliest Israelites long before there was a sub-category of Israelite called "Jew". Only a tiny percent of Jews are "Orthodox".
Type (2) The much larger group of "Reform Jews" who do not rigorously follow the religious precepts handed down from the earliest Israelites. They follow a modified type of Deity worship, if any, and are primarily 'Humanists'. Reform Judaism does not believe the Torah was written by G-d. Few Reform Jews claim to be 'seriously religious'.
SECULAR or CULTURAL Jews: A "Cultural Jew" is one who enjoys the
ethnic, social, cultural, political and perhaps even religious aspects of being
"Jewish". These "Jews of Convenience" may or may not have genetic Israelite
roots.