MySQL difference between wait_timeout and connect_timeout

Right from the MySQL Documentation

• wait_timeout : The number of seconds the server waits for activity on a noninteractive connection before closing it.
• connect_timeout : The number of seconds that the mysqld server waits for a connect packet before responding with Bad handshake

EXAMPLES

• If wait_timeout is 1800 (30 Minutes), the DB Connection will close in 30 minutes if the connection is idle (indicated by Sleep in the command column of the processlist).
• If connect_timeout is 10, then mysqld will reject you if you cannot login (authenticate) in 10 seconds.