The 2Checkout purchase routine sets a cookie on the user’s computer when they begin a purchase. This cookie remembers what the customer had placed into their cart. This way, if the customer loses their Internet connection or is otherwise unable to complete their order, they are not forced the entire checkout process over when they come back to finish their order.

Because you are using the same computer, you may see items in the cart from the previous order. Your customers will not see this because they are using different computers and Customer #2′s computer will not have the cookie set by Customer #1′s computer.