HEBREW vs. ISRAELITE vs. JEW vs. SEMITE — WHAT THESE WORDS ACTUALLY MEAN
As concisely as I can:
These are genealogical terms; they refer to particular lineages, or family trees, and descend as subgroups of each other.
To begin with, you have the man named “Shem”. It would be more consistent to either spell his name “Sem” or to spell “Semite” as “Shemite” and “Sumer” as “Shumer”, since all those words are properly pronounced with an initial “sh” sound. (British archaeologists and historians in the 18th or 19th century decided that “Sumer” had a nicer ring to it than its real pronunciation, hence my having to explain this now.) Shem and his descendants are Semites.
(All of the Arabic races descend from Shem, by the way. All Arabs are Semites.)
Several generations of Shem’s descendants later, there is born one named “Ever”. Too briefly, the transposition runs: Ever/Eber/Ivriim » Heber/Ibaru » Hebrew. Ever and his descendants are Hebrews.
Hebrews are also known as Jews.
Several generations of Ever’s descendants later, there is one born named “Jacob”. Jacob was the son of Isaac and grandson of Abraham, and later changed his name to “Israel”. Jacob/Israel and his descendants are Israelites. And now you know why the Israelites are so often called “the Children of Israel” — it’s not a stylistic attempt at grandeur, it’s a precise genealogical description.
I’ve been dealing with these subjects my entire life. I’ve forgotten more about the so-called “Biblical” texts and the doctrines derived from them than people holding divinity doctorates ever learn in the first place. This particular subject is preschool-level for Biblical scholars worldwide, so ignore the fake “neonazi” disinformation agents who want to colonize your mind with some whackjob/hackjob version of these facts.