Part time off grid
A part time off grid solar, wind or otherwise system feeds electricity directly into the grid, offsetting the amount of electricity supplied by the grid. If the amount of electricity produced by the system is greater than the amount being used by the business or residence, the excess is fed into the grid resulting in the account being credited by the amount fed in, causing the grid to act as a sort of electrical bank.
Conversely, when the system is producing less electricity than the consumer is using, the grid makes up the shortfall, debiting the consumer's account.
The benefit of an on grid system is that the consumer will reduce their electricity bill while still having the grid as a backup supply. Of course, in the event of a blackout, unless the consumer has a battery bank to use as a backup supply, they'll be left without power if the system isn't producing any.
This is generally the cheapest type of system to install, unless a battery bank is included as part of the system.
Full time off grid
A full time off grid system has no connection to the grid whatsoever and must rely on its on system for its electricity supply, and, since there is no grid to fall back on at nighttime or when the systems aren't producing sufficient power to supply the consumer's needs, a battery bank is used to store excess power for later use.
For this reason, an off grid system tends to be more expensive simply due to the amount of equipment needed to build such a system. In addition, most off grid users also use a backup generator in case of emergency, adding further to the cost of an off-grid system.