Was Jesus a Jew or a Hebrew?
All Jews are Hebrews. Jesus was both a Jew and a Hebrew. The
term "Jew" referred to the people of Judea, of which Jesus was a
member, and was used as early as the fourth century BCE (including
in the book of Esther).
All Jews were Hebrews (since a Hebrew is any descendant of Eber
and Eber is an ancestor of Abraham, Isaac, and Jacob, the ancestors
of the Jews), but not all Hebrews were Jews. Jesus was also more
strongly aligned with the Pharisees he rejected than any of the
other contemporaneous Jewish movements. Although the Pharisees
would not become the dominant form of Judaism until the Talmud was
published, their views and methods of interpretation were certainly
well-developed by Jesus' time.