Semite =/= Hebrew =/= Israel =/= Judea =/= Jew =/= Judean =/= Judahite
Noah had three sons; Japheth (Indo-Europeans), Shem (Semites) and Ham (Hamites). Japheth would spawn the white peoples who would inhabit lands from Western Europe to India, Shem would spawn the white peoples who would live in Mesopotamia, and Ham would spawn the white peoples who would live in North Africa. Semites are those descending from Shem, including Babylon.
Abraham would leave Ur in modern day Iraq, Babylon. Abraham founded a new nation, his people were called the Hebrews. Thus a Hebrew is a Semite, but a Semite need not be a Hebrew.
Israel is the name that Jacob (son of Isaac, son of Abraham) received from God in an event that foreshadows Baptism. He wrestles with God, being forced to confront all of his past evils, and leaves the event physically changed and spiritually reborn; with the new name Israel.
Israel then becomes an overall term to include all of the tribes of Israel. Jacob/Israel had 12 sons, Joseph would have two sons Ephraim and Manasseh who received Jacob/Israel's blessing (as he had received Isaac's blessing, and Isaac had received Abraham's). Judah was the fourth son, and is the one who came up with the idea to sell Joseph - the favoured son - into slavery for some shekels. So an Israelite is a Hebrew, but a Hebrew need not be an Israelite.
When the Hebrews controlled the Holy Land the land it was originally split between each of the tribes. Broadly speaking you had 10 in the North in what was called Israel, and you had the Judahites and Benjaminites (and later Levites) in Judea. Israel is conquered by the Assyrians, a divinely ordained destruction sent from God due to their sins including child sacrifice. Judea also partook in these practices but were given another chance, Jesus, after which they too would be destroyed. No matter how you slice it; geographically Judea was not the country Israel, though Judah is one of the tribes of Israel.
People born in Judea were called Judeans, whether they were a Judahite or not. A Judahite being a member of the tribe of Judah. We know that Paul of Tarsus was of the tribe of Benjamin, yet he is still also called a Judean because of living in Judea, though he was not a Judahite. Jesus was both a Judahite and a Judean, but neither of these are synonymous with Jew.
The term Jew did not exist until later on, with the religion of Judaism actually being younger than Christianity. At the time of Jesus and in the New Testament we learn of a sect of the Hebrews called the Pharisees. The Pharisees uniquely followed the Oral Torah, which is today codified as the Talmud, which instructed them do all manner of strange things (including lying to non-Hebrews, manipulating them, enslaving them and stealing from them). Jesus condemned these as the traditions of men, and condemned the Pharisees as hypocrites, a brood of vipers, and the children of the devil. The other Hebrew sects required the Levites, that is the Priest class, to perform their rituals in the Temple; without the Temple they cannot perform their rituals, and essentially the faith is dead. The Pharisee's Oral Torah allowed for them to not worship at the Temple. Thus when the Temple is destroyed in 70AD by the Romans, as prophesied by Jesus; there is a crisis in the Hebrew world. They have two options; either become a Christian with Jesus as the Temple, or else become a Pharisee with the Oral Torah which states they do not need a Temple. This is the event that births Judaism, a Jew is an adherent of Judaism, and Judaism is essentially Pharisaism. So one can be a Judean and a Judahite without being a Jew; Jesus being the prime example, as Jesus clearly detested Pharisaism and considered it of the devil.