There is no essential difference between "not selected" "save" and "charge" modes. All three cycle the engine to charge the battery.
The difference is that:
No button pressed - The engine will charge the battery to remain at the lowest permitted level after you run it down.
Charge pressed - The engine will attempt charge the battery to the highest possible level.
Save pressed - The engine will attempt to keep the battery charged to the level that it had when "save" was selected (but in practice the level will drop slowly)
This way you can control the amount of charge during and at the end of your journey - if you have no need of EV operation, let it run down to empty by not selecting a charge mode.
If you have to drive some distance on EV, select the save when the battery is at the level that you will need for the (last) EV bit.
If you need as full a charge as possible (e.g. with a long urban distance at the end, or an emission-controlled zone ahead, or a hilly bit, etc.) select "charge"
In general I like to run the car in charge mode all the time (except the last bit) on motorway journeys and in the mountains. Actually save can be fine too in these cases, depending on the circumstances.
There are claims that the car runs most efficiently with the battery half-full, but the differences will be small, and I have never seen it.