1. God separates the light from the darkness, the earth from the water, and creates all the plants and animals and peoples of the world.
2. The LORD God creates the garden of Eden, makes Adam from mud and Eve from his rib, plants a tree of knowledge and tree of life, etc.
Already there's a divergence: Adam is supposedly the first man in the second story, but in the first story, all the peoples of the world have already been created. But the more interesting divergence is in the name of the responsible God. This often flies over the head of readers in English, but notice that the first story isn't the "LORD God", just "God". This is because in Hebrew, the name of God in the first story is "Elohim", while in the second, it's "YHVH" -- a name too holy for Jews to pronounce, so they just say "Hashem" ("the name"), although if you're naughty you can say "Yahweh" or "Jehovah" or whatever. Why the difference?
A clue is that "Elohim" is a pluralised word in Hebrew. Once Judaism became fully monotheistic, this became interpreted as something like "The Wings of God" -- a sort of abstract all-encompassing Godly aura, rather than the pointed and personified manifestation of the divine, which is YHVH. But this is a bit of a tortured post-rationalisation, and isn't explicitly supported by the text. It's much more straightforward to read "Elohim" as simply "the gods", which is probably how it was read when the text was first assembled, with a henotheistic YHVH text being appended to an earlier polytheistic text.
Even the first commandment -- "I am YHVH, your God, and you shall have no other Gods before me" -- reads better as a henotheistic rather than a monotheistic text. It doesn't say there are no other gods. It pretty strongly implies the opposite. It just says that the other gods aren't for you.