Can server differentiate user computers?

[cyberbaffled]

On the "Thank You" page there's this notice: "Thank you for shopping. Please click the Log Off link to ensure that your receipt and purchase information is not visible to the next person using this computer."

Does this imply that the server cannot differentiate user computers such that if a session is terminated by any means other than using Log Off -for example, terminated by using a browser's "close" utility, or interruption of router signal, or a "time out"- the possibility exists that the chronological next server connection using a different computer begins with the previous user's account information plus receipt and purchase information?

[DrByte]

I'm not sure I understand your question.

It's basically the same message as what a bank website tells you: please logoff to protect your privacy.
They say that regardless of the fact that the session is set to expire when closing the browser ... because clicking Logout IS more secure than merely letting a timeout happen.

(In case you want clarification of the technicality behind why a Logout is more secure than a timeout, it's because if somehow someone has hijacked your banking or shopping session without you knowing, if you click Logout then that forces a logout on the server-side too, effectively killing a hijacker's access)