Executing "nagios start" from the command line and getting some output idicates that you have "nagios" in roots path. Verify this with "which nagios"
So, since the binary "nagios" is in your path, executing "nagios start" means execute nagios with the options "start" and for nagios, this means use the config file called "start". Since you are in the directory /etc/rc.d/init.d nagios assumes that is where the config file is located.
Now, if you want to actually execute the init script named nagios, then do this: