On hybrid inverters/AIO's the circuits after the inverter (that are technically off-grid if you set off-grid in the AIO) are called critical load panels, and if power is lost the critical load panels are all that will be getting power from the inverter. And if in off-grid mode hybrid inverters use an internal transfer switch (relays) that never have grid connected to the critical loads while the inverter is running and hence switching from grid to inverter and back has a quick power blip. In off-grid mode the solar/batteries/inverter can only power the critical load panels
Hybrid AIOs are not the same as Off Grid AIOs. An off-grid AIOs does not have 'switches' or 'software' settings to connect their output to the grid. There is no path for the AC generated to reach the grid. An example of an off-grid AIO is an MPP Solar 3048LV unit - I have one in my trailer. An off-grid AIO may take in grid but will not push out to the grid.
I agree that a Hybrid AIO (like Sol Ark) is different and I'm not up what they do exactly as all my equipment and experience is 100% off-grid. However, I'm guessing you can wire a Hybrid AIO such as Sol Ark as 'off-grid mode' where there's no physical wiring to send AC out to the grid.... Maybe someone can clarify this.
A critical loads panel is typically a physical sub-panel (not physically part of an AIO) that's used as a mechanism to separate circuits from the main panel so the incoming power to the sub-panel can come from different (selectable) sources - grid, or generator, or off-grid power as examples. This is what I ment above when I said one can take a home circuit and disconnect it from the main panel and power it from off-grid power. An MTS is an example of a critical loads sub-panel that let's you choose the source of power for individual circuits instead of all or nothing.
You can think of an Off Grid AIO as working like this.....
Grid ------> AIO ----- charge battery ----> battery -----> inverter ---> AC output ---> home circuits (critical load sub-panel perhaps)
Solar ----->
Thus, it's easy for an off-grid AIO to have built-in ATS/UPS because it can invert from the battery all the time.... so if the grid goes down (and there's no solar panel power) the battery is no longer being charged but that doesn't affect the battery --> inverter ---> AC output until the battery runs down.
Yes, an off-grid AIO can have an option to bypass (the battery) but then it's....
Grid ---> AIO ---> home circuits (critical load sub-panel perhaps)
In no case is the off-grid AIO AC output making it's way back to the grid as can happen in grid-tie.