There are a number of subtle differences between the creation stories in Genesis 1 and 2 that show their differing purposes. Noting the differences between these stories can help us to avoid confusing the origins of Adam (the distant ancestor of Jesus) from the origins of mankind (a scientific question which is touched upon in Genesis 1 only).
1. In Genesis 1 the animals are created before humans appear on the scene. This is consistent with the scientific record. But in Genesis 2 God (poetically) fashions a man out of the ground prior to the fashioning of the animals. This is a clue to the reader, that the subject matter of the two stories is not identical.
2. In Genesis 1 God makes men and women at the same time. In Genesis 2, God fashions Adam out of the ground before he (poetically) fashions a woman out of the rib of Adam.
3. In Genesis 2 it is clear that Adam and Eve are a particular human couple. This is by no means clear in Genesis 1:26-27. The text could be describing a particular human couple, but it is equally open to describing an original human population, which is more in keeping with 1:20-25 (describing the original populations of fish, birds and mammals prior to man).
4. In Genesis 1 men and women rule God’s world together with equal authority, whereas in Genesis 2 the woman is fashioned to assist the man (v. 18), and Adam expresses his authority over Eve by assigning to her a descriptive name (v. 23). Verse 20 strikingly compares the woman to the animals, in the sense that she is there as a suitable “helper” for the man, only after it is determined that none of the animals can do so.
5. In Genesis 1 human beings are told to multiply and fill the earth, and exercise dominion over it. In Genesis 2, Adam is created specifically to take care of God’s Garden/Sanctuary in the location of Eden (2:5-8).