If I recall correctly:
BAT switch ON, Standby switch on AUTO: Battery supplies standby AC bus via inverter and standby DC if main power is lost.
BAT switch OFF, Standby switch on AUTO: Standby AC and DC buses are de-energized when main AC is lost.
Standby switch on BAT: Standby buses powered from battery regardless of BAT switch position or state of main sources. The battery will be float charged by the battery charger as long as it is supplied with AC.
Standby switch OFF: AC and DC standby buses de-energized regardless of main source states.
These are the settings one will normally encounter. There is a (complex) truth table that describes the state and source of each bus, depending on main AC bus and source states, switch positions, the type of battery system (single or dual), air-ground logic, etc. But I seem to have misplaced my copy after leaving Boeing.
