Off grid solar power system doesn't connect to the power grid. In general, it includes solar panels, charger controller, batteries and inverter. This system will store the solar power into the batteries, batteries energy will be converted the electricity power to supply the appliances working through the inverter. 

On grid solar power system connects to the power grid. In general, it includes solar panels, grid-connected inverter, the solar power will be converted the electricity power to appliance working directly. When the solar power is off, the power grid will replenish the electricity power to appliances working.