offgrid inverter
takes energy only from solar, charges batteries, and provides electricity for home use. is completely disconnected from grid and for remote area usage.
grid tie / on grid inverter, takes electricity from grid and solar, provides electricity to your home and feeds back excess electricity to grid. it will shut off when there is no power in grid. its primary use is for saving your overall cost of electricity.
hybrid is a mix of both types. it has grid tie features, but also has batteries for energy storage. it will take electricity from solar, grid. and provide electricity for your home and charging batteries. in absence of grid, your home is powered by solar and battery, in case of no grid, no solar, you will have power from batteries. you can set priority for each energy source, set charging voltages etc.