The only difference is in how the file is packaged for delivery. For a Mac, they package the firmware file and the instructions into a .DMG file that MacOS opens like a Disk Drive, and mounts on the desktop. For Windows, they place the files in a .ZIP archive.
Almost any Mac can open and extract files from .ZIP archives, but a Windows PC generally won't be able to deal with a .DMG file.
The Firmware file (and the instructions, for that matter) is the same for both. It has to be, because the camera doesn't come in Mac or PC Editions!