The difference is the response from qmail and what it does with the message.
Reject:
<mail@domain.com>:
111.111.111.111 does not like recipient.
Remote host said: 550 sorry, no mailbox here by that name. (#5.7.17)
Giving up on 111.111.111.111.
This message comes from the sending SMTP server, rather than your Plesk box meaning the email never enters your mail queue. 0 emails fully processed by your server. Your Plesk box will refuse to accept the message saving data transfer.
Bounce:
<mail@domain.com>:
This address no longer accepts mail.
This would be a standard bounce message from the Plesk mailserver, similar to an autoreply really but the original message is deleted. The email entered your mailqueue then was returned to the sender - 2 emails fully processed by your server.