How does the save system work?

The game saves after every progression in game, like doing any kind of mission, playing a mini-game or doing fixer contracts. Pretty much everything saves the game, even taking money out of an ATM.
Look for this icon on the left side of your screen, whenever you see it, it means the game is being saved.

The game does not save when you purchase skills, pick up new guns, or find money (such as inside vehicles). The game saves after story missions, although I'm not sure if it saves just the story or other things as well. The game seems to save after side missions, but it doesn't seem like skills or guns are saved after these missions; you must still sleep in order for them to be saved. I'm not sure if this is how it works for everyone, or if I have a bug on mine.