Generally speaking, the terms Hebrews, Jews, and Israelites all refer to the same people- the nation which sprang from Abraham through Isaac and Jacob, a nation promised and chosen by God in the Old Testament (Genesis 12:1-3). Each term emphasizes some aspect of this people's origin or background.
The term Hebrew is first used in the scriptures to refer to Abraham (Genesis 14:13). Then it is used of Joseph (Genesis 39:14,17) and the other descendants of Abraham through Isaac and Jacob (Genesis 40:15; 43:32). It is uncertain why Abraham is called ~'the Hebrew." Some have suggested that the word Hebrew comes from a word meaning 'on the other side" or "to cross over" and alludes to Abraham leaving Ur and crossing the Euphrates River. Furthermore, no special reason is given in the scriptures for calling the nation that came from Abraham through Isaac and Jacob, Hebrews. The term does, however, identify the nation as descendants of Abraham. It has been suggested by some that Hebrews is the national name that was preferred by this nation and the name by which foreign nations often referred to it (lnterDretation of I and II Corinthians, 2 Corinthians 11:22, Lenski; Lange's Commentary, 2 Corinthians 1:22)
The name of Jacob, the son of Isaac (Genesis 25:26) who was the promised son of Abraham (Genesis 17:19), was changed to Israel when he wrestled with a man of God (Genesis 32:28). Hence, the descendants of Abraham through Isaac and Jacob (Israel) made up the nation of Israel and were sometimes called Israelites (Exodus 9:7). When the nation divided, the ten northern tribes arrogated to themselves the name Israel, and the two southern tribes became known as Judah. Both nations were taken captive; Israel was taken captive by the Assyrians and Judah was later taken captive by the Babylonians. When the Babylonian captivity ended, exiles of both nations- Israel and Judah- returned to their homeland and were again united under the designation of Israel.
The term Jews was first used to describe the inhabitants of Judah, the name taken by the two southern tribes of the nation of Israel during the division (2 Kings 16:6; 2 Kings 25:25). After the Babylonian captivity, the meaning was extended to embrace all of Israel. It is suggested by some that this name may have been given to all Israel at this time because the larger portion of the remnant of the covenant people were from Judah (New Unger Bible Dictionary). Jew or Jews is often used to contrast or to distinguish this nation from Samaritans, Gentiles, or proselytes (John 4:9; Romans 2:9; Acts 2:10).
All three of these terms- Hebrews, Isreelltes, and Jews-continued to be used in the New Testament to describe the fleshly descendants of Abraham through Isaac and Jacob (2 Corinthians 11:22; John 4:9). Furthermore, since the Israelites were God's chosen people of the Old Testament, in the New Testament the terms Jew and Israel are occasionally used figuratively to represent God's chosen people today- the spiritual seed of Abraham, the church (Galatians 3:29; Romans 2:27,28; 9:6). A careful study of the context of New Testament passages will allow one to discern which way the terms are used in the New Testament and of whom they speak. There are only a few times in the New Testament that a special meaning is given to the words.
The terms Hebrews, Israelites, and Jews are close synonyms and are often used interchangeably. All three terms refer to those who have descended from Abraham through Isaac and Jacob. The terms are used figuratively a few times in the New Testament in reference to the spiritual seed of Abraham. When speaking of the fleshly nation of Israel, the term Hebrew ties the people directly to Abraham; Israelite relates them to Jacob, or Israel, and Jew or Jews reminds us of this people's homeland and is used to distinguish the race from other people or to contrast them with others.