First of all, one minor correction: /mac/bin/startup SHOULD BE either /mac/bin/startmac or /mac/bin/startmac24
The "ShutDwnPower" and "ShutDwnStart" routines documented in the "A/UX Toolbox: Macintosh ROM Interface" are WRONG! The routines behave the same as Mac OS Shutdown Manager routines (shutdown and restart).
To Logout from user's login shell, use the AUXDispatch() trap with the A/UX_LOGOUT selector. All definitions for the AUXDispatch trap are specified in the header file /usr/include/mac/aux.h.
For more detailed information about AUXDispatch trap, please refer to page 3-15 on "A/UX Toolbox: Macintosh ROM Interface" documentation.