A hybrid solar system is a grid-tied solar system that also has a solar battery for energy storage. These can give the best of both worlds because you can store excess energy in a battery for backup power during a blackout, or to use during expensive evening peak electricity pricing hours. The advantage of still having the grid connection is that you don’t need to 100% rely on your solar and battery. This means you can have a smaller and cheaper energy storage system compared to the same home that is completely off the public grid system.
Net metering does economically what a solar battery does physically, allowing you to store the economic value of your excess solar energy (kWh credits) for use at night without the cost of physically storing the electricity. So for 99% of homeowners currently connected to a public grid, a simple grid connect system will be what you want.