A back-up system is an electrical apparatus that provides emergency power to a load when the input power source or mains power fails.
An off-grid solar system (off-the-grid, standalone) is the obvious alternative to one that is grid-tied. For homeowners that have access to the grid, off-grid solar systems are usually out of question.
Grid-tied, on-grid, utility-interactive and grid back-feeding are all terms used to describe the same concept – a solar system that is connected to the utility power grid.