An on-grid or grid-tied solar system is a system that works along with the grid. This means that any excess or deficiency of power can be fed to the grid through net metering.
You will always have power either from the solar system or from the grid. They do not have batteries.
Off-grid systems work independently of the grid but have batteries which can store the solar power generated by the system.
The system usually consists of solar panels, battery, charge controller, grid box, inverter, mounting structure and balance of systems.
A solar hybrid system stores your excess solar energy and can also provide backup power during a blackout.
This is perfect for home owners although, for the majority of businesses that operate during the daylight hours, a common grid-feed solar system is still the most economical choice