the logging setup will determine what gets logged into the controllers logs, and is thus made eligible for sending to syslog
the syslog level is the 'filter' that chooses from what the controller is logging
e.g.
if 'user' logging is set to level info, and syslog is set to level debugging, then you get all info logs from 'user'
if 'user' logging is set to level debugging and syslog is set to level 'warning', then none of the "debug" or "info" logs will be sent to syslog, but they will still be logged in the controller logs
Likely what you want is that the syslog severity is set to debugging, and then you control what goes in by selection the correct "logging" setup. Note that if you try to set logging level 'debugging' on multiple categories (e.g. system, security, user) you will cause high CPU (or system instability). Therefore you should exercise caution if plan to collect logging level 'debugging' all of the time and try to narrow it down using subcat and process masks.
said another way - it's usually not advisable to turn on debugging and try to collect everything - you should establish the things you are looking to collect (say for example you want to keep info about IP to mac address mapping and associations) and then try to find that information in "info" level logs first and try to avoid the urge to enable "debugging" (especially in system and security categories)