See studies by F. F. Bruce (rev. ed. 1988) and W. L. Lane (1991).
Hebrews (or Hebertes, Eberites, Hebreians, "Habiru" or "Habiri"; Hebrew: עברים or עבריים, Standard ʿIvrim, ʿIvriyyim Tiberian ʿIḇrîm, ʿIḇriyyîm) are an ancient people defined as descendants of biblical Patriarch Eber (Hebrew עברי (ʿIḇrî) "traverse or pass over"), a great-grandson of Noah.
They were called Ibri, meaning the people from over on the other side of the Jordan river. They lived in the Land of Canaan (the Levant). The Ibri people are also known in Africa, mainly Egypt and Sudan.
Other authors believe that Ivri is another name for Abraham, and define the Hebrews as the descendants of this patriarch. Note however that Abraham is once referred to as "Abram the Hebrew" (Genesis 14:13).
Hebrews are known as the ancestors of the Israelites, who used the hebrew language. Israelites were the writers of the Hebrew Bible and therefore the spiritual and historical forerunners of the Jews, Christians and Muslims. In the Bible and in current language, the word Hebrews is often used as a synonym for Israelites, and sometimes for the users of the hebrew language (Jews and Israelis).
Israelites are defined as the descendants of Jacob, son of Isaac, grandson of Abraham. Eber, an ancestor of Jacob (6 generations removed), is a distant ancestor of many people, including the Israelites but also the Arabs, descendant from Ishmael. Among historical scholars, there is some disagreement about the relationship between the Hebrews and Israelites, the history and legacy of the Hebrew people.
The terms "Hebrews" and "Israelites" usually describe the same people, called Hebrews before the conquest of the Land of Canaan and Israelites afterwards. Occasionally, "Hebrews" is used to designate the Jews, who use the hebrew language. The Epistle to the Hebrews was probably written for Jewish Christians. The current State of Israel, a homeland for all Jews, is often nicknamed the "Hebrew state".