Hagar and the son in the desert
Not equivalentBiblical text
Gênesis 21:8-21
8And the child grew, and was weaned: and Abraham made a great feast the same day that Isaac was weaned.
9And Sarah saw the son of Hagar the Egyptian, which she had born unto Abraham, mocking.
10Wherefore she said unto Abraham, Cast out this bondwoman and her son: for the son of this bondwoman shall not be heir with my son, even with Isaac.
11And the thing was very grievous in Abraham’s sight because of his son.
12And God said unto Abraham, Let it not be grievous in thy sight because of the lad, and because of thy bondwoman; in all that Sarah hath said unto thee, hearken unto her voice; for in Isaac shall thy seed be called.
13And also of the son of the bondwoman will I make a nation, because he is thy seed.
14And Abraham rose up early in the morning, and took bread, and a bottle of water, and gave it unto Hagar, putting it on her shoulder, and the child, and sent her away: and she departed, and wandered in the wilderness of Beersheba.
15And the water was spent in the bottle, and she cast the child under one of the shrubs.
16And she went, and sat her down over against him a good way off, as it were a bow shot: for she said, Let me not see the death of the child. And she sat over against him, and lift up her voice, and wept.
17And God heard the voice of the lad; and the angel of God called to Hagar out of heaven, and said unto her, What aileth thee, Hagar? fear not; for God hath heard the voice of the lad where he is.
18Arise, lift up the lad, and hold him in thine hand; for I will make him a great nation.
19And God opened her eyes, and she saw a well of water; and she went, and filled the bottle with water, and gave the lad drink.
20And God was with the lad; and he grew, and dwelt in the wilderness, and became an archer.
21And he dwelt in the wilderness of Paran: and his mother took him a wife out of the land of Egypt.
Qur'an
Ibrahim 14:35-37
وَإِذْ قَالَ إِبْرَٰهِيمُ رَبِّ ٱجْعَلْ هَـٰذَا ٱلْبَلَدَ ءَامِنًا وَٱجْنُبْنِى وَبَنِىَّ أَن نَّعْبُدَ ٱلْأَصْنَامَ
35And when Abraham said: My Lord! Make safe this territory, and preserve me and my sons from serving idols
رَبِّ إِنَّهُنَّ أَضْلَلْنَ كَثِيرًا مِّنَ ٱلنَّاسِ ۖ فَمَن تَبِعَنِى فَإِنَّهُۥ مِنِّى ۖ وَمَنْ عَصَانِى فَإِنَّكَ غَفُورٌ رَّحِيمٌ
36My Lord! Lo! they have led many of mankind astray. But whoso followeth me, he verily is of me. And whoso disobeyeth me - Still Thou art Forgiving, Merciful
رَّبَّنَآ إِنِّىٓ أَسْكَنتُ مِن ذُرِّيَّتِى بِوَادٍ غَيْرِ ذِى زَرْعٍ عِندَ بَيْتِكَ ٱلْمُحَرَّمِ رَبَّنَا لِيُقِيمُوا۟ ٱلصَّلَوٰةَ فَٱجْعَلْ أَفْـِٔدَةً مِّنَ ٱلنَّاسِ تَهْوِىٓ إِلَيْهِمْ وَٱرْزُقْهُم مِّنَ ٱلثَّمَرَٰتِ لَعَلَّهُمْ يَشْكُرُونَ
37Our Lord! Lo! I have settled some of my posterity in an uncultivable valley near unto Thy holy House, our Lord! that they may establish proper worship; so incline some hearts of men that they may yearn toward them, and provide Thou them with fruits in order that they may be thankful
In common
Both texts speak of the same family: Hagar and her son, left in an arid land under God's direct care. Genesis narrates the episode with rich detail: the expulsion, the water running out, Hagar's despair, and an angel who shows her a well. The Qur'an, on the other hand, doesn't narrate this scene at all: the only direct point of contact in the text is a prayer of Ibrāhīm's (14:37), in which he recalls having left part of his offspring "in a valley without cultivation," near the Sacred House, asking God to care for them.
Differences
It's important not to confuse what the Qur'an's text says with what the wider Islamic tradition adds afterward. The well-known story of Hagar running between the hills of Safa and Marwah searching for water, and the appearance of the Zamzam well, isn't in the Qur'an's text: it comes from later reports (hadith), not from the revealed text itself. That's why this comparison is marked "not equivalent": the Qur'an and the Bible aren't telling the same scene with different details, the Qur'an simply doesn't narrate this scene. What the Qur'an does is briefly and retrospectively acknowledge that this family existed and was left near what would become Mecca, tying it to the spiritual founding of the Kaaba, a dimension the biblical text doesn't have, since for the Bible the story of Hagar and Ishmael ends in the wilderness of Paran, with no connection to any shrine.
Biblical text: Genesis 21:8-21, Jewish-Christian tradition.
Qur'an and hadith: Verse 14:37 is the only point of contact in the revealed text; the Zamzam and Safa-Marwah narrative comes from hadith (namely Sahih al-Bukhari), not from the Qur'an.