Off grid
Off Grid systems are completely independent from the traditional electricity grid. People living with off grid systems produce all their own electrical energy and consume only what they're able to produce. System components include an energy source (such as solar panels), a storage medium (like a battery), and usually an inverter to create high quality electricity for standard household appliances. A fossil fuel burning generator can be incorporated into an off grid energy system with great success.
Grid Connected
A Grid Connected system has a passive connection to the standard electrical grid used to charge batteries either in the absence of a renewable energy source or in addition to a renewable energy source. A backup power system, designed to bridge gaps in standard electricity service, is a grid connected system.
Interactive / Grid Tie
Grid Interactive means that power can flow back and forth between a renewable energy system, your loads, and the standard electricity grid. Energy you require but can't produce is drawn from the standard electricity grid and energy you produce but don't consume is sent onto the grid. This is the basis for 'net metering', an arrangement where your electric utility credits your account for electricity you send into the grid.