Basically the two systems work like this...
Off the Grid systems use a stand alone Inverter IE the Solar Cells (or wind genny or whatever) supply the Battery Bank and the Battery Bank supplies the Inverter which converts the DC into AC power for the house on demand.
Off the Grid systems need a Battery Bank because there is no grid to import elektrikery from.
Grid connect systems use a Grid Tie system IE there is no battery bank and the Solar cells supply the Inverter which runs at optimum power and "in phase" with the Grid.
Any 'extra' power available from the Inverter not consumed by the house is exported back to the Grid by a "smart meter".
When the power available from the Inverter drops off (as the Sun sets, the wind drops or your Nuclear Reactor Scrams) then the house needs more power than the Inverter can produce so the "smart meter" imports power from the Grid
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