These are the first-born children of both Abraham and Isaac. Hagar gave birth to Ishmael but he was not considered the “promised child” and Esau (see Three Books and The Day) sold his birthright to Jacob. So neither of these men received the rights of the first-born; this is in agreement with the shadowing of Adam and Jesus. ( FYI Muslims say they are the spiritual children of Abraham through Ishmael.) You can read that both of these men maintained a relationship with their fathers because both of them showed up to help bury their fathers; Genesis 25:9 for Abraham and Genesis 35:29 for Isaac. Josephus, a Jewish historian, actually uses the death of Isaac as a dividing point for his history book The Antiquities of the Jews.
Ishmael is an interesting “type and shadow” he was born from an Egyptian and got an Egyptian wife; Egypt for Christians is associated with our bondages and addictions before we are saved. So even though Egypt still holds that shadow Ishmael takes on an added shadowing because he is something personal/family in our lives. One of the last mentions of him is in Genesis 25:18 which refers to the fact that his descendants lived in hostility (or to the east of) all of their brothers. According to Josephus Ishmael became the father of the Arabians. (see Part 2)
Now the Arabians do show up later in Scripture in some interesting places. In 2 Chronicles 17 Jehoshaphat has tribute brought to him by Arabs, Jehoram is attacked by them in chapter 21, and in chapter 26 Uzziah is beating them again with God’s help. Nehemiah has trouble with them because of Geshem and they are mentioned in Isaiah, Jeremiah, and Ezekiel where they are condemned to the sword or are under God’s wrath. But a scripture that ties all of this together is in Galatians 4:21 – 31. Hagar represents Mount Sinai (the Law) that is in Arabia and Paul links that to physical Jerusalem while the heavenly Jerusalem is linked to Sarah.
References:1.12.2 The Antiquities of the Jews, Zondervan NIV Exhaustive Concordance