With a grid-tie connection, the property uses mains power provided from the nationwide power grid as a secondary power source. It generates DC power from solar panels, sends that power through an inverter which converts it into mains power which is used within the home or passed back to the national grid. This is passed back power is referred to as selling back.
With an off grid setup other than your solar panels you'd use some other source of secondary power for times when the sun's not shining. Options include a generator, wind turbine, hydro-power or battery backup each of these systems has its own pro's and con's but each situation for their use and or cost, duration, return on investment will differ. The main schematic difference between a grid and off-grid though is an off-grid generates DC power which it stores in batteries using a charger (the name of the charger will change depending on what your charging source is. A solar array uses a solar controller, wind and hydro both use controllers (in fact all 3 use the same model controller in different ways so if you have multiple sources of generation you will require multiple controllers) All these controllers essentially charge your batteries, one might say solar/charge controller or wind/charge controller. These batteries are used to provide power and flatten out the curves of either low power generation times or high power usage from multiple appliances all being used at the same time. The second part of an off-grid system is the generation of mains power onsite, rather than coming from the grid it is converted from DC power (the batteries power). This is just like the inverter used in a grid-tie setup to convert the solar DC power to mains AC power.