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

This version includes game 4.0 because any complete package is version 4.0. Copy the HD files into the game folder, run Heroes3HDSetup.exe, and you'll see Heroes32.exe in the Executables folder. Select the resolution, and in "Your HoMM3 version," choose GoG.com Complete (No CD). Be sure to click OK or Apply and Launch. To play the HD version, run Heroes32.exe_HD.exe; to play the non-HD version, run Heroes3.exe version 4.0.

I have a follow-up question. You mentioned that when launching Heroes32.exe_HD.exe, it requires a disc. How does it do that? Does a Windows window pop up, or does the game launch, and then a Heroes window appears on top of the main menu? If it's the second option, does this happen with a modified resolution or with the standard 800x600 resolution?