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Google counts a conversion when someone goes from google to a site and converts.
Google counts a transaction when someone converts within 30 days of clicking on an ad (and this can be multiple for the same person).
Some affiliate programs give credit to the first cookie placed on a computer.
Some affiliate programs give credit to the last cookie placed on a computer.
Therefore, if you're using an affiliate program that counts a conversion as the first cookie on a computer, and someone goes from your AdWords ad to a site and converts, you'll see a conversion in your adwords account, but you won't get the affiliate credit for the sale.