OFF Grid refers to a power system that generates electricity from a solar array and stores this electricity in batteries. The stored energy is fed to utilities using inverters.
ON grid / Gridrefers to a power system which is connected to a power grid. The electricity generated by the solar array is fed to utilities using grid tied inverters. If the electricity generated by the solar array is more than the requirements of the utilities then it will be fed to the grid. If the demand of the utilities is more than the electricity generated by the solar array, the balance requirement of power will be drawn from the grid.
Grid Tie with battery backup refers to a power system that has the advantages of both an off grid and a grid tied system. When grid power is available it serves as a normal grid tied system and charges the battery also. In the event of a grid power failure the utilities are fed power from the battery. Once the grid power is restored, it behaves as a normal grid tied system and will charge the batteries again.