Are those Google's definitions or yours?
The reason I ask is that after reading your answer and running a custom report they look to be:
Conversions are the first sale recorded
Transactions are the initial sale plus any subsequent sales upto 30 days later but potentially on the same visit as the first sale.
I wonder how many people like me have been comparing Adwords Conversions with Overture Conversions by mistake?
Google assigns the sale to the day the click occurred (i.e. If I click today, but next week, today will be credited with the sale).
Overture assigns the sale to the day the sale occurred.