It is presenting two different perspectives of the same event. We see parallelism throughout the Bible where one account of something is told and then repeated again in another way. We see this done across books, across chapters, even in the next verse. Just because there are multiple approaches conveyed does not necessarily mean they are from different authors. Just because something else is repeated in a different way does not mean one person is not the author of both.
The first and second chapters have different purposes.
Then, attending to just those creative events mentioned in both chapters, the following divergences are evident. Genesis 1 has water first, then land, followed by plants, animals, and finally humans (’adam, consisting in male and female together). By contrast, Genesis 2 begins with the existence of land, then comes water, followed by a human (’adam, later specified as a man, ’iš), then plants, animals, and finally a woman (’iššâ).’
The first chapter follows an organizational, chronological tone whereas the second chapter is more lyrical and differs on its focus from general creation (the focus of Genesis 1) to the specific sixth day.
First, careful analysis reveals that there is deliberate purpose in the individuality of these two sections of Scripture. In Genesis 1 there is a broad outline of the events of the creation week, which reaches its climax with the origin of mankind in the very image of God. In Genesis 2 there is the special emphasis upon man, the divine preparation of his home, the formation of a suitable mate, etc. Edward J. Young has a good statement of this matter:
There are different emphases in the two chapters…but the reason for these is obvious. Chapter 1 continues the narrative of creation until the climax, namely, man made in the image and likeness of God. To prepare the way for the account of the fall, chapter 2 gives certain added details about man’s original condition, which would have been incongruous and out of place in the grand, declarative march of chapter 1 (1960, p. 53).