Automatic power switching, grounds not connected
the grounds may not be connected.

I hope it's meant that the main and backup supplies' grounds may not be connected.
Here's a concept diagram:



simulate this circuit &ndash; Schematic created using CircuitLab
Main and Backup supplies do not share the grounds here. CONTROL BLOCK is supplied from the Main supply. This block drives the relay and directs the SYSTEM's input to the Main supply by default. When the CONTROL BLOCK decides the Main supply is faulty (e.g. too low voltage) or the Main supply is not applied (i.e. unavailable) then the relay's contacts will switch to NC position and the SYSTEM will get the supply input from the Backup supply.
hth.