Your question revolves around the discrepancy of details when reading Genesis 1-2 sequentially. In a strictly literal reading of these two texts together, it creates some obvious problems, one of which being the question of when humans, particularly men and women, were created. Some readers came to the idea that because Eve is specifically formed in Genesis 2, after man and woman have already been made in Genesis 1, that there must have been a previous woman. In Medieval Judaism, she was identified as 'Lilith'.
This is a historical reading of Genesis 1-2, but the interpretation is rejected by nearly all modern critical scholars, for a variety of reasons, but the most direct one being: No such 'Lilith' or 'first woman before Eve' is specified anywhere in Genesis, or any other biblical text.
The Two Creation Accounts
There was another question some time back asking about the authorial intent of Genesis 1; my answer is here, and can be summarized as such: Genesis 1 is a temple creation text, with the universe as God's temple that he 'rests' in (on the seventh day)
When we read Genesis 2, it is not a sequel to chapter 1. The vocabulary is different, the name used for God is different, the order in which God creates things is different. As such, Genesis 1 and Genesis 2 should not be understood as happening in a sequence, nor should Genesis 2 be understood as taking place 'on the sixth day' of Genesis 1. Each creation account was written by an entirely different author, for entirely different reasons.
What we have are two entirely different stories.
What Genesis 1 describes is the creation of humanity, both men and women, after all the plants and animals have already been made, and that's that. What Genesis 2 describes is the creation of man (just the one), after which God creates the plants and animals, and only when none of them are found to be 'suitable' for the man does God created woman.
While both creation texts have something to say about humanity, and men and women, what it is they are saying is distinct and unrelated to what the other says. The 'seven days' are not a part of the Genesis 2 creation text.