Most Bible scholars generally accept the notion that Genesis 1 (more than verses 1 & 2) give an "overview" of creation, while Genesis 2 gives more detail, focusing in on Adam, Eve, and the critters. Another theory, not well accepted by the "young Earth" believers, is that there is a "gap" between Genesis 1 and Genesis 2. See the Related Link "Wikipedia: Gap Creationism" for more information. _________________________________
One of the many problems with the "gap" theory is that if GOD had created another Earth before this one, then it would show Him to be imperfect and that what He created was flawed and thus rendering all of GOD's Word to be incorrect because we read in Genesis 1:31 "And God saw every thing that he had made, and, behold, it was very good." If there was a "gap" between 1 & 2, why would God destroy the "very good" creation and keep the flawed one? It is only after the fall in chapter 3 that the only creation mentioned in The Bible stopped being "very good." Romans 5:12 "Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned:" So, since what Romans tells us is correct, it was because of the fall of man that death entered the world. Man was created to live forever in fellowship with GOD and the fall separated man from GOD and it was Jesus who came and bridged the gap between sinful man and Holy GOD. So if there was a "gap" between chapters 1 & 2 in Genesis then death would have been before the fall of man and not after thus making the Holy Word of God untrue, but since we know that death is a real fact of life we also know that before the fall there was no "gap" and no death.
So, therefore, it is safe to say that the creation account recorded in Genesis:
# Shows the "general" overall record of creation
# and then zero's in on the details of that creation.