That set up is typically called an emergency inverter. It takes in line voltage, charges a rack of batteries and in the event of a power failure it outputs AC line voltage to feed lights like a generator would. I have done some of these in stores that had no place for a generator.
Storage battery set ups are in my experience different, they take line voltage charge the batteries and in the event of a power failure they output low voltage DC to feed large numbers of low voltage emergency lights via multiple low voltage circuits all around the building.
I have done these in some theaters. They have the advantage of centralized batteries for servicing but you need to run large conductors for voltage drop in separate raceways .
Both the inverter systems and the storage battery systems need to be listed as emergency equipment.