What is the origin of the name Israelite Hebrew and Jew?

Answer 1

1) Israelite: a descendant of Israel. Jacob, the grandson of Abraham, was given the name Israel by God (Genesis ch.35).

2) Hebrew: this title was used concerning Abraham (Genesis ch.14). It means a descendant of Eber (see Genesis ch. 10-11).

3) Jew: a descendant of Judah. Judah was one of Jacob's sons (Genesis ch.29); and, after most of the Israelites (the Ten Tribes) were exiled by the Assyrians to points unknown, the majority of the remainder were (and are) of the descendants of Judah.

Answer:

"Hebrews" (Ivrim) means descendants of Eber (Ever). Ever was an ancestor of Abraham (Genesis ch.10-11) and the earliest Hebrews were Abraham's uncles and cousins for several generations back. They were among the Western Semites and lived in northern Mesopotamia, near the confluence of the Balikh and the Euphrates.
Abraham himself is called a Hebrew (Genesis ch.14) because of his ancestors, not because he was the first one. That is the simple meaning of Genesis 14:13. Poetically, however, Abraham is called Ivri because the name also translates to "other side." Abraham was figuratively on "the other side" since he was the only monotheist (Midrash Bereshit Rabbah 42:8) until his teachings took root. His ancestors and cousins had slipped into idolatry well before his time, as is evident from Genesis 31:30, 31:53, and Joshua 24:2.
The word Hebrews can continue to refer to Abraham's descendants until the lifetime of Jacob. After that, we prefer "Israelite," since Jacob was given that name (Genesis ch.35), which is considered a national title; one of honor. "Israelite" refers to the people (Jacob's descendants) down to about the time of the destruction of the First Temple some 2500 years ago.
"Jews" refers to the people from Second Temple times, up to this day, because after the Assyrian conquest the remaining Israelites were (and are) mostly from the Israelite tribe of Judah. But all the above terms are occasionally interchanged.

In modern usage, we use the term Hebrew only to refer to the language.

Answer 2

Same people, different eras. "Hebrews" (Ivrim) actually means descendants of Eber (Ever). Ever was an ancestor of Abraham (Genesis ch.10-11) and the earliest Hebrews were Abraham's uncles and cousins for several generations back.
In 1934-39, excavations were conducted at ancient Mari on the Euphrates River. They found that ancient towns were named after the ancestors of Abraham: The city of Nahor was found near the city of Harran which exists to this day. Equally clear signs of early Hebrew residence appear in the names of other towns nearby: Serug (Assyrian Sarugi), Terah (Til Turakhi, "Mound of Terah"), and Peleg (Paliga, on the Euphrates). All these names are found in Genesis ch.11.
Abraham himself was called a Hebrew (Genesis 14) because of his ancestors, not because he was the first one. That is the simple meaning of Genesis 14:13. Poetically, however, Abraham is called Ivri because the name also translates to "other side." Abraham was on "the other side" since he was the only monotheist (Midrash Rabbah 42:8) until his teachings spread.
In that sense, "Hebrews" is often used to refer to Abraham's Israelite descendants. Thus it refers to the Jewish people.
"Israelites" refers to the people down to about the time of the destruction of the First Temple some 2500 years ago. "Jews" refers to the people from Second Temple times onward, because after the Assyrian conquest the remaining Israelites were (and are) mostly from the Israelite tribe of Judah.

Answer 3

"Hebrews" (Ivrim) means descendants of Eber (Ever). Ever was an ancestor of Abraham (Genesis ch.10-11) and the earliest Hebrews were Abraham's uncles and cousins for several generations back. They were among the Western Semites and lived in northern Mesopotamia, near the confluence of the Balikh and the Euphrates.
Abraham (18th century BCE) was called a Hebrew (Genesis ch.14) because of his wider family.

Poetically, however, Abraham himself is called Hebrew because that name (Ivri) also translates to "the other side." Abraham was figuratively on "the other side" since he was the only monotheist (Midrash Rabbah 42:8) until his teachings took root. His ancestors and cousins had slipped into idolatry well before his time, as is evident from Genesis 31:30, 31:53, and Joshua 24:2. For that reason, Jews do not bestow on them the honorific title of ancestors despite the genealogical connection.
We credit Abraham as our first ancestor despite knowing exactly who came before, since it was Abraham who founded our beliefs. Thus, "Hebrews" is often used to mean Abraham and his Israelite descendants, instead of his wider family. In this sense it can refer to the Jewish people.

• Link: Abraham's biography
  

The word "Hebrews" can continue to refer to Abraham's descendants until the lifetime of Jacob. After that, we prefer "Israelites," since Jacob was given that name by God (Genesis ch.35), and it is considered a national title; one of honor. "Israelites" refers to the people (Jacob's descendants) down to the Assyrian conquest (133 years before the destruction of the First Temple), some 2600 years ago.

• Link: Jewish ancestry
  

"Jews" refers to the same people, from the end of First Temple times up to this day, because after the Assyrian conquest the Israelites who remained in the land were (and are) mostly from the Israelite tribe of Judah, and the land was then called Judea. But all the above terms are occasionally interchanged.

In modern usage, we prefer to use the term "Hebrew" only to refer to the language.