What is the difference between a birth right and a blessing as in the story of Esau and Jacob?
A birthright referred to a person's inheritance. For most of the world's history, the first born child of a family would receive an extra inheritance from his father. What would happen is that when a father died, they would count his surviving children and add one to the count. They would then divide the inheritance that many ways and the eldest child would get two portions. Thus, if a man died having three surviving children, his inheritance would be divided four ways. The eldest child would receive two-fourths (that is, one-half) of the estate, and the other two children would receive one-fourth of the estate each.
The birthright can be seen in this Mosaical law: "But he shall acknowledge the son of the unloved wife as the firstborn by giving him a double portion of all that he has, for he is the beginning of his strength; the right of the firstborn is his" (Deuteronomy 21:17). The double portion came as a right of birth; that is, by the right of being first born.
This is what Esau sold to Jacob for a bowl of red bean stew when he returned hungry from a hunting trip (Genesis 25:29-34). Now Isaac their father was a very wealthy man. Esau gave up half of his inheritance (one-third of Isaac's estate) for a single bowl of red bean stew. This is why it is mentioned, "Thus Esau despised his birthright" (Genesis 25:34).
Though not commonly done, a birthright could be given to another son. For example, "Now the sons of Reuben the firstborn of Israel-he was indeed the firstborn, but because he defiled his father's bed, his birthright was given to the sons of Joseph, the son of Israel, so that the genealogy is not listed according to the birthright; yet Judah prevailed over his brothers, and from him came a ruler, although the birthright was Joseph's" (I Chronicles 5:1-2). Because Reuben had sex with his father's concubine, Jacob took away his second portion and gave it to Joseph. He did this by making Joseph's own children count as his children. Since Joseph had two sons, those sons each got a portion of Jacob's estate; thus giving Joseph's family a double portion.
The family blessing was a way to designate who became the head of the extended family when the father died. Like the birthright, the blessing generally went to the eldest son but not always. Again using Jacob's family, Reuben should have received the blessing, but because of his sin, he was skipped. Next in line was Simeon, but he and his brother Levi (third in line) had destroyed a town in anger over the rape of their sister. For that Jacob decided that they were not suitable to lead the family. Therefore, the blessing came to Judah. Thus, in Jacob's family the person receiving the blessing and the person receiving the birthright (or double portion) were two different people.
A change in the blessing also happened in Isaac's family. Before Isaac's twin sons were born, God said, "Two nations are in your womb, Two peoples shall be separated from your body; One people shall be stronger than the other, And the older shall serve the younger" (Genesis 25:23). Because God placed the older son under the younger son, he was stating that the second born was to receive the blessing. Now Isaac in his old age decided to change this and give the blessing to his eldest son, Esau, anyway. However, his wife overheard his plan and arranged it so that Jacob tricked Isaac into thinking he was his brother. Thus Isaac gave the blessing to his second son, just as God said, even when he tried to go against God.
The blessing in Abraham's descendants was particularly important because God stated to Abraham that from his descendants the Savior of the world would come. The blessing followed the path of those who were Jesus' ancestors. Jesus was a descendant of Judah, who had received Jacob's blessing (Hebrews 7:14).