Genesis 1:26 - So God created man (Hebrew - 'âdâm) in his own image. In the image of God he created him; male and female he created them. *this use of "Adam" is done in the generic "humankind" sense.
Genesis 2:7 - Then the LORD God formed the man (Hebrew - 'âdâm) of dust from the ground and breathed into his nostrils the breath of life, and the man (Hebrew - 'âdâm)became a living creature. *see also verse 15-16, same context
Genesis 2:20 - The man (Hebrew - 'âdâm) gave names to all livestock and to the birds of the heavens and to every beast of the field. But for Adam (Hebrew - 'âdâm) there was not found a helper fit for him. * The same word here is translated differently in the first section and the second. It's also worth pointing out that in some translations, such as the KJV, both words are translated as "Adam", including earlier in verse 19 even though the ESV and NIV *my other two Bible copies* translate verse 19 as "the man".
The difference in these translations is context. In chapter 1 there is a clear reference to "man" and then broken into "male and female", which strongly implies humankind as the context. For chapter 2 I would assume that up until Eve enters the picture there is no need to call Adam by anything other than "the man". But once the writer brings up a helper for him, the name becomes personal. That would be my assumption. Either way, the Hebrew is the same and since that is the original that is more important than any English translation we may have.
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