A Brief History of Israelites, Hebrews, and Jews

According to the Bible, the first monotheist was Abraham. He passed on his belief to his son Isaac, who passed it on to his son Jacob who received the name Israel. Whether you believe they were actual historical people or mythologic characters, those men are considered the patriarchs of our people.
According to the Bible, the Israelites (incidentally, the English language has 2 words, Israelites for the ancient people and Israelis for the citizens of modern Israel, but in Hebrew it is one word) migrated into Egypt to escape a famine. The government of Egypt was friendly to them at that time. A later government was unfriendly to the Israelites. Moses led the Israelites out of Egypt to a period of wandering in the desert to the land east of the Jordan River (the location of modern day Jordan), and ultimately, after the death of Moses, the Israelites migrated westward across the Jordan into Canaan (the land situated between the Jordan River and the Mediterranean). The historians tell us that a people from Asia called the Hyksos entered Egypt and ruled the country or part of it for a period of time, and were then driven out of Egypt by the native Egyptians. So the Biblical and historical accounts of those events are somewhat compatible. What is important as far as our names are concerned is that word Hebrew means crossing over. To the Canaanites, the Hebrews were the people who came from across the Jordan River.
The Hebrews eventually formed the Kingdom of Israel which consisted of various territories inhabited by the various tribes of Israel. Later the kingdom split into two, the northern kingdom which retained the name Israel and the southern kingdom which took the name of its most prominent tribe, Judah (Judaea). The northern Kingdom of Israel was later conquered by Assyria and its people disappeared. The Kingdom of Judah was later conquered by the Babylonians, but some Jews returned after Babylonia was defeated by the Persians and formed the new Kingdom of Judaea until it was conquered by Rome with the ultimate dispersal of Jews into the diaspora for the past 2000 years. The present state of Israel was declared in 1948 following a period of migration of Jews into the territory mainly beginning in the late 19th Century.
So, the name Israelite (Israeli) dates back to around the time of our ancestors entering, living in, or leaving Egypt, Hebrew dates back to the entrance of our people into the land of Israel after the death of Moses, and Jew dates back to the time of the kingdom of Judah (Judaea). The Jewish religion evolved over the various periods described above, but Judaism as we now know it might be said to date from the time of the Kingdom of Judaea.