The traditional order is more like

    # /etc/init.d/myserver reload
    unknown command reload
    # /etc/init.d/myserver restart
    unknown command restart
    # /etc/init.d/myserver stop
    myserver: warning: frobulator did not fully unfurl
    # /etc/init.d/myserver start
    myserver: still running on pid 1234
    # kill -TERM 1234
    kill: (1234) - No such process
    # grep "running on pid" /etc/init.d/myserver
            echo "$0: still running on pid `cat /var/run/myserver.pid`"
    # rm -f /var/run/myserver.pid
    # /etc/init.d/myserver start

What you're calling "traditional" is the minor, purely UI-facade-level consistency we got after 10 years trying to clean that mess up. But actually we eventually gave up, and went on to invent something better.