The word "Hebrew" is of uncertain origin. Some scholars define it as meaning to traverse or pass over. There is evidence that the term was applied to long distance traders even before the word's first usage biblically in Genesis 14:13 ("Abram the Hebrew").  Other scholars believe Hebrew referred to Shem's son Eber (Genesis 10:21 (NLT), "Sons were also born to Shem, the older brother of Japheth. Shem was the ancestor of all the descendants of Eber." Wherever the word originated, Jesus was of Abraham's lineage. Matthew 1:1, "The book of the generation of Jesus Christ, the son of David, the son of Abraham." Therefore, one might correctly state that Jesus was a Hebrew.

The word "Jew" comes from the word "Judah." Judah was one of Jacob's (Israel's) twelve sons and Jesus was a descendant of Judah. Matthew 1:1,2, "The book of the generation of Jesus Christ, the son of David, the son of Abraham. Abraham begat Isaac; and Isaac begat Jacob; and Jacob begat Judas (Judah in the Hebrew language)." Judah received a special blessing from his father. Genesis 49:10, "The scepter will not depart from Judah, nor the ruler’s staff from between his feet, until he to whom it belongs shall come and the obedience of the nations shall be his." The scepter and ruler's staff was promised to our Lord Jesus through the line of Judah. This prophecy will be fulfilled when Jesus reigns as King on earth and all the nations obey Him.

In summary: Jesus was a Hebrew from the line of Judah (a Jew).