There are some people today who believe that these terms mean different things, but in actuality, they are really synonymous. There have been many false theological concepts that have developed over the years based on a simple misunderstanding of these terms. So, we will do a basic study of definitions to get to the heart of the matter, using Easton’s Bible Dictionary as a source.
In the Bible, there are three terms that are used to describe the same people, Jew, Israelite, and Hebrew. The name “Hebrew” is a name applied to the Israelites in the Bible used by foreigners (Gen 39.14, 17, 41.12). It is also used by the Israelites themselves when talking to a foreigner (Gen 40.15, Exo 1.9). In addition, it is used when compared to other nations (Gen 43.32; Exo 1.3, 7, 15; Deut 15.12). In the Brit Chadasha (renewed covenant) the same contrast exists (Acts 61; Phil 3.5). The name “Israel” is given to Jacob after his struggle at Peniel (Gen 32.28) because as a “prince,” he had power with God. This is the most common name given to his descendants. All twelve tribes are called “Israelites” or the “children of Israel (Josh 3.17, 7.25; Judges 8.27; Jer 3.21) and also the “house of Israel” (Exo 16.31, 40.38). This name is sometimes used for the “true Israel” (Psa 73.1; Isa 45.17, 49.3; John 1.47; Rom 96, 11.26).
After the death of Saul, the ten tribes took this name for themselves as if they constituted the whole nation (2 Sam 2.9, 10, 17, 28, 3.10, 19.40-43) and the kings of the ten tribes were called “kings of Israel” while the kings of the other two tribes were called “kings of Judah.” After the exile, the name Israel was used for all twelve tribes. The name “Jew” comes from Judah, a son of Jacob. It was first used to designate one from that tribe or to the kingdom of Judah (2 Kings 16.6, 25.25; Jer 32.12, 38.19, 40.11, 41.3). It is used in contrast to those belonging to the kingdom of the ten tribes, who were called Israelites. While in Babylon, and after, the name was given to all twelve tribes (Est 3.6, 10; Dan 3.8, 12: Ezra 4.12, 5.1-5). At the beginning, the people were called Hebrews until after the exile when the name was not used much. Paul described himself as a Hebrew in 2 Cor 11.22 and Phil 3.5, an Israelite in 2 Cor 11.22, and a Jew in Acts 21.39 and 22.3 however.
So, in conclusion, there were three names used in the Brit Chadasha to describe those who have descended from the twelve tribes. The name “Jew” in regards to their nationality and to distinguish themselves from the non-Jews, and “Hebrews” in relation to their language, customs, and lifestyle to distinguish themselves from the Greek-speaking Jews. This contrast can be seen in the book of Acts very clearly in Acts 6.1. The name “Israelite” will be used when they are described as a people chosen by God and the mandate they have to teach the nations about God, the Messiah, and the redemption (Rom 9.4-5). All three names are used to describe the descendants of Jacob or those that came from any of the twelve tribes. confusion over these biblical definitions exists today and it is caused an “identity crisis” with many believers. Several denominations today believe they are “Jews” or “Israelites” when in actuality they are not. This type of belief comes from a severe lack of teaching at one end, and a severe lack of personal study of the Scriptures on the other. Somehow, some believe they are lacking in something, have fallen short spiritually, or feel “left out” of something if they are not considered “Jewish.” As a result, there are movements that develop like the “Two-House” and “Hebrew Roots” movements and others. In actuality, God doesn’t care either way and that is quite clear from the Brit Chadasha where Paul says in 1 Cor 7.17-20 that we should walk as God has assigned us. If someone is “circumcised” or Jewish, let him not seek “uncircumcision”, and if one is called “uncircumcised (non-Jewish) let him not seek “circumcision” (or to become Jewish). He says circumcision or uncircumcision doesn’t mean anything, but the keeping of the commandments do, as they apply to both groups. Peter came to the same conclusion in Acts 10.35 where he says that God is not partial to anyone (Jew or non-Jew) and he who “fears him and does what is right (keeps the commandments as they apply to each one) is welcomed by him.” A non-Jew who believes in Yeshua is grafted into the commonwealth of Israel and they should follow a Torah-based faith in him, which means they are to follow the Torah as it applies.