On-grid solar systems are the simplest and most cost effective way to connect PV modules to regular utility power. Grid-Connected systems can supply solar power to your home and use utility power as a backup. When you produce more power than you use, your surplus green / renewable electricity goes into the grid to be used by others. When you use more energy than you produce or at night when your solar panels do not produce, power produced by your utility is sent to you via the grid. No matter what size system you have, you do not have to make any lifestyle changes.
Off-grid systems are generally employed in remote locations without utility grids. It's a good solution in an area where running a line to the local utility grid is prohibitively expensive, or an area where blackouts and brownouts are relatively common. With an off-grid system, your solar energy system would supply all of the power a cabin, home or business would need.
Off-grid systems completely relieve you from dependency on electrical grids. Off-grid systems typically require a larger up-front investment than grid-tie systems. This is, in large part, due to the greater demands on the system. A grid-tie usually supplements a home's energy demands, reducing the amount of energy required from the utility grid. An off-grid system is responsible for providing all power - appliances, lighting, and the electricity required for other utilities.
Off-grid systems are generally larger than grid-tie systems. To be fully independent, a system must have a greater array of energy-producing panels, which in turn requires more batteries to store the charge and more equipment to regulate the charge. While requiring more parts will require a large initial investment, in the long-run an off-grid system may save you thousands.