4.7.8: Official Definition
4.X.X
[RFC3463] (Standards Track) from the The Internet Engineering Task Force (IETF) definition for codes that start with 4.X.X:
A persistent transient failure is one in which the message as sent is valid, but persistence of some temporary condition has caused abandonment or delay of attempts to send the message. If this code accompanies a delivery failure report, sending in the future may be successful.
X.7.8
[RFC3463] (Standards Track) from the The Internet Engineering Task Force (IETF) definition for codes that end with X.7.8:
This response to the AUTH command indicates that the authentication failed due to invalid or insufficient authentication credentials. In this case, the client SHOULD ask the user to supply new credentials (such as by presenting a password dialog box).