A net zero home can be on-grid (net metered) or off-grid. Earthships are net zero homes. They create all their own power as well as harvest their own water and deal with their own waste products. This is truly net zero, but probably not suitable for the average homeowner.
Heat Your Home w/ Solar Hot Water - This is close to our plan. The only difference is we plan on being able to flush the system with cold water as our floors will be cement and we can cool our floors also. :)