The items on the right column prefer to work with alternating current. That is provided by an inverter. The items at the right column may need to operate at night, possible when panels are not productive but their daylight production was stored in the batteries.
As already explained, the battery stores the energy from the solar, making it MUCH more useful - and the inverter converts it to mains AC to run normal household equipment.I think they should either use only the inverter or you should use the battery, both device store power that supplies to home devices. that's why I am confused,
I have a question The voltage coming out of the solar array is AC or DC. I assume there will be an AC voltageNo. Only the battery stores power (or more correctly energy). The inverter converts the panel DC voltage or the battery DC voltage to an AC voltage for AC loads (most mains-powered devices).