HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

I didn't quite understand your point, could you clarify?

The autosave feature saves the game at the end of your turn and the beginning of your opponent's turn (you click the clock icon, and that's the beginning of their turn). Your opponent's saves are the opposite – at the end of their turn and the beginning of yours. So, if you want to see the situation at the beginning of one of your turns, you need to ask for their save files.