The creation stories that are located at Genesis 1:1 and Genesis 2:6 do contain significant differences - most obvious of these is the order of things happening.

The first creation story (the well known one) happens along these lines:

  1. Heaven and Earth, Light and darkness divided
  2. Division of the water from the firmament
  3. Creation of dry land, grass, herbs, trees
  4. Stars in the sky, Sun and Moon
  5. Creation of birds and whales
  6. Creation of cattle, things that creep, man and woman
Specifically, within Genesis 1, man and women are created in verse 26-27:
  • 1:26 And God said, Let us make man in our image, after our likeness: and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepeth upon the earth.
  • 1:27 So God created man in his own image, in the image of God created he him; male and female created he them.

Within Genesis 2, Man is created on verse 7. After this point, in Genesis 2:19, the animals are created, followed by woman in verse 21-22.

  • 2:7 And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.
  • 2:19 And out of the ground the LORD God formed every beast of the field, and every fowl of the air; and brought them unto Adam to see what he would call them: and whatsoever Adam called every living creature, that was the name thereof.
  • 2:21 And the LORD God caused a deep sleep to fall upon Adam, and he slept: and he took one of his ribs, and closed up the flesh instead thereof;
  • 2:22 And the rib, which the LORD God had taken from man, made he a woman, and brought her unto the man.

Clearly, there is a different order of events between these two stories. However, what does it matter? These are stories about creation - every culture has them, and every culture's creation stories are different. These stories are not exact accounts of the happenings at the beginning of time, nor were they meant to be. This is not science but rather faith. The story in Genesis 1 tells of the categories of things - there is light and darkness, there is water and land, there are trees, there are beasts that live on the land and beasts that live in the sea and sky. These are all of the things that existed to the writers and account for the sabbath, and makes the claim that God created everything there is. Thats it - nothing else. Don't read more into this than an account of the types of things that are and a statement of faith that they were created by God.