One
theory regarding the writing of Genesis is that it was not written by
Moses, in the exact order that the chapters and verses go today.
According to this theory, Genesis is a mixture of ancient Hebrew writings by at least three different sources. Genesis 1 was written by what is known as the "priestly" source; this style was common to ancient liturgical writings. This chapter holds the creation story that would more likely be used in formal worship services.
Genesis 2 was written by the "yahwist" source, which was more devotional or didactic in nature. This is kind of more the "Bible study" creation story, had the Hebrew people had Bible studies back in the day.
Naturally, this comes from a school of thought that doesn't necessarily take every word of the Bible literally, but asks, "What meaning did this have for the original audience, and what meaning does it have for us today?"