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

In my opinion, 3.2 and 4.0 are the versions of the "Heroes 3" executable (3.2 - The Shadow of Death, 4.0 - Complete Collection). It's likely that you and your opponent have different versions.

Well, I downloaded it from heroes3.tv, probably like everyone else. I checked, and I also have 4.0.0.0.
And the game doesn't complain about the game version, but about the hotfix. If I disable the hotfix completely, it lets me log in, but I don't know what will happen during the game; I haven't checked. I don't want to play without the hotfix.
The fact that this issue pops up no matter who I log in with clearly indicates that the problem is on my end, but I can't figure out what I need to fix :D