Hybrid mode = Using engine, while maintaining the battery charge. Going uphills and starting to move, uses battery while downhill and braking charges back.
EV mode = Full battery movement. Engine is used only, if you really push the pedal down or enougth to move to "power" section.
Auto = Basically ( how I feel it works is, that it melts the battery first then goes to hybrid mode.
In normal day, when I know battery is enought for my driving, I use EV mode only. When I know There's long journey, I try to manually set depending on the situation. I never keep it auto.