"In the Hebrew Bible, the term "Israelites" refers to the direct descendants of any of the sons of the patriarch Jacob, or of the people called Israel, and of a worshipper of the God of Israel, Yahweh. In the period of the divided monarchy it referred only to inhabitants of the northern kingdom, and is only extended to cover people of the southern kingdom in post-exilic usage.[11] Other terms sometimes used include the "Hebrews" and the "Twelve Tribes" (of Israel).
The term Hebrew (עברי) has Eber as an eponymous ancestor. It is used synonymously with "Israelites", or as an ethnolinguistic term for historical speakers of the Hebrew language in general.
*An eponym is a person, place, or thing for whom or for which something is named, or believed to be named.
https://en.wikipedia.org/wiki/Eponym
*Ethnolinguistics (sometimes called cultural linguistics)[1] is a field of linguistics which studies the relationship between language and culture, and the way different ethnic groups perceive the world.
https://en.wikipedia.org/wiki/Ethnoreligious_group
Yahweh tells Moses that if Pharaoh refuses to let the Hebrews go to say to Pharaoh "Thus says Yahweh: Israel is my son, my first-born and I have said to you: Let my son go, that he may serve me, and you have refused to let him go. Behold, I will slay your son, your first-born". Moses returns to Egypt and tells Pharaoh that he must let the Hebrew slaves go free. Pharaoh refuses and Yahweh strikes the Egyptians with a series of horrific plagues, wonders, and catastrophes, after which Pharaoh relents and banishes the Hebrews from Egypt. Moses leads the Israelites out of bondage[49] toward the Red Sea, but Pharaoh changes his mind and arises to massacre the fleeing Hebrews."
The Jews, which include the tribes of Judah, Benjamin, Simeon and partially Levi, are named after the southern Israelite Kingdom of Judah. The word "Jews" is found in Kings (16:6),Chronicles (I, 4:18), and in numerous passages in Jeremiah, Zechariah and the book of Esther.[12] The Samaritans, whose religious texts consist of the five books of the Samaritan Torah (but which do not contain the books comprising the Jewish Tanakh), do not refer to themselves as Jews, although they do regard themselves as Israelites, in accordance with the Torah."
https://en.wikipedia.org/wiki/Israelites#Biblical_Israelites
The term "Israeli", is actually a transliteration of the Hebrew word ישראלי. This does not give an accurate understanding of what the word represents.
"In Judaism, an Israelite is, broadly speaking, a lay member of the Jewish ethnoreligious group, as opposed to the priestly orders of Kohanim and Levites. In texts of Jewish law such as the Mishnah and Gemara, the term יהודי (Yehudi), meaning Jew, is rarely used, and instead the ethnonym ישראלי (Yisraeli), or Israelite, is widely used to refer to Jews. Samaritans commonly refer to themselves and Jews collectively as Israelites, and describe themselves as the Israelite Samaritans."
https://en.wikipedia.org/wiki/Israelites#Biblical_Israelites
*An ethnoreligious group (or ethno-religious group) is an ethnic group whose members are also unified by a common religious background. Ethnoreligious communities define their ethnic identity neither by ancestral heritage nor simply by religious affiliation but often through a combination of both.
The use of the term "Israeli", as it appears in the English language press, is an attempt to disassociate the modern day "Jewish" people from traditional "Israelites" and "Hebrews". As a modern day ethnoreligious group, the "Jewish" people have separated themselves from the Biblical Israelite family by placing more emphasis on the "religious" aspect of the term "ethnoreligious", whereby the adherence to "Judaism" is the principal requirement for recognition as a member of the "Jewish" people.
Speaking to members of the Jewish community can be confusing as times; when referring to the times of the Patriarchs and Moses, they freely use the term "Jewish" when speaking of the people, until they reluctantly refer to those whom Moses led out of Egypt as "Hebrews". the term "Jews" stated as appearing in the Book of Kings and a few others above, actually comes from the word יהודי in Hebrew. Based on the information that a ישראלי (Yisraeli) is viewed as referring to an "Israelite", a יהודי, logically, would be a "Yehudi", or Judite.
-ite1
suffix
1.
forming names denoting natives of a country.
"Israelite"
https://www.google.co.il/search?q=suffix+-ite&oq=suffix&aqs=chrome.1.69i57j69i59j0l4.5893j0j8&sourceid=chrome&es_sm=0&ie=UTF-8#newwindow=1&q=meaning+of++-ite
Thus, the term "Jew" is a very poor transliteration of "Yehudi". Ultimately, all of the seed of Jacob are not only "Israelites", but also, at their ethnolinguistic root, "Hebrews", or "עברים". Even if a person views him/herself ethno-religiously as a "Jew", he/she is no less ethno-linguistically a "Hebrew". Today, the official documents of the citizens of Israel list this citizenship as ישראלית in Hebrew, yet says "Israeli" in English, which is clearly a transliteration, not a translation. Therefore, the current state of Israel is already an "Israelite" nation.
"19 say into them: Thus saith YHWH GOD: Behold, I will take the stick of Joseph, which is in the hand of Ephraim, and the tribes of Israel his companions; and I will put them unto him together with the stick of Judah, and make them one stick, and they shall be one in My hand.
21 And say unto them: Thus saith YHWH GOD: Behold, I will take the children of Israel from among the nations, whither they are gone, and will gather them on every side, and bring them into their own land;
22 and I will make them one nation in the land, upon the mountains of Israel, and one king shall be king to them all; and they shall be no more two nations, neither shall they be divided into two kingdoms any more at all;"
Ezekiel 37
The land that is spoken of above is the land known today as "Israel". This land was given to the seed of Abraham, thru Isaac, Jacob and finally Jacob's 12 sons. This land is the collective possession of the whole family of Jacob/Israel, and are collectively known as "Israelites", "Hebrew Israelites" or as the "Children of Israel". The religion they collective received from YHWH thru Moses would be better termed as "Hebrew Israelite Fundamentalism", for the people the instructions were given to were clearly both "Hebrews" and "Israelites". This is what the returned "House of Israel", i.e. the Northern Kingdom, would claim as a part of their ethno-religious heritage.
The Nation that would be the result of the reunification of the two houses would carry the name "The Nation of Israel", and the people collectively be called "Israelites", "Hebrew Israelites" or the "Children of Israel". Each family will have its individual identity as well; those of the family of Judah would still be "Yehudites", of the family of Levi "Levites", of the family of Dan "Danites" and of Ephraim "Ephraites". Or, each family could collectively decide what form their common name would take. The reunification would have to be done in such a way that none of the sons is slighted.
"13 The envy also of Ephraim shall depart, and they that harass Judah shall be cut off; Ephraim shall not envy Judah, and Judah shall not vex Ephraim."
Isaiah 11
One family of Hebrew Israelites living in one Hebrew Israelite Nation.