In the time of Jesus, there was a split between the Talmudic Israelites (whose religious leaders where the Pharisees) and Israelites who did not concede legitimacy to the Talmud. The latter included the Sadducees, the Zealots, and the Essenes
The Pharisees became dominant, and defined "Jewish" to mean Israelites who grant validity to the Talmud
Also there are Israelites who reject books later than five books of Moses, they are called Samaritans and there are two villages still surviving. They are the actual Israelites, the others are Judeans.