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

The difference is that when the AI chooses how to move, it also has moments where randomness kicks in (at least when the AI calculates the value of an attack target, which is essentially present in any battle). Therefore, in auto-battle/quick mode, the randomness shifts due to the generation of random numbers when choosing the target for the Titan, which doesn't happen when the Titan is controlled by a player.