A normal inverter system or a UPS basically have batteries to store energy from the grid when the supply is available. When the power is cut off, the inverter takes the DC power from the batteries and converts it into AC used by the appliances. There is an automatic control in the system that intellects if the grid is not supplying power and switches the UPS or inverter into battery mode.
Grid connected inverter
A grid tied solar inverter, also converts DC power (produced from Solar Panel) to AC. But additionally they have built-in MPPT (Maximum Power Point Tracking) feature. As the voltage produced by Solar Panel varies depending on the temperature and obtainability of sun, MPPT allows solar inverters to draw maximum power from the solar panels. The solar inverter used for grid-connected system also comprises an anti-islanding functionality which basically means that the inverter is designed to shut down if the grid goes down, so that you won’t be inadvertently energizing the grid if a someone is working on it