The latter. When a message is sent, the recipient is specified separately. The "To" header does not necessarily reflect the recipient.
However the "To" header may be modified when the message is being delivered. You see, "Jane" is not an e-mail address. So to make it an e-mail address, a hostname needs to be added, thus you'll get "To: Jane@hostname" if the message headers were originally "To: Jane". Sometimes you'll even get spam addressed as "To: Buy@hostname, Our@hostname, Crap@hostname" because of this.
Perl / MySQL / HTML+CSS