An off-grid system is not connected to the electricity grid and therefore requires an off grid solar inverter with a battery storage. The inverter continuously draws DC power from the battery bank and convert it to AC power which powers your AC load in the house. The high cost of batteries and off-grid inverters means off-grid systems are much more expensive than on-grid systems and so are usually only needed in more remote areas that are far from the electricity grid.
Hybrid inverters are a hybrid between the traditional on-grid inverters and off-grid inverters. During normal daytime operation the hybrid inverter synchronizes with your mains utility power. The inverter will then supply power to your loads and recharge your battery storage using primary the solar panels during the day and secondary use Eskom when the panels don't deliver enough power. In addition to this cost saving during daylight hours, batteries are used to supplement your usage during the evening hours.
The grid-tied inverter control system will automatically convert the DC power generated by the solar panels into the AC power needed by your property's load. To comply with grid regulations the system will normally be configured to ensure that no energy is exported back to the grid, but this can be changed if your electricity supply contract allows you to sell power back to your supplier. Grid-tie inverters are required by law to shut down during a utility outage and will then not produce any power coming from the panels. These inverters do not have a battery back up and the main purpose is to reduce your electricity bill. These systems are more suited for businesses where most of the power is used during daylight operation.