I have heard expressions such as ".NET FAT32 client" or ".NET FAT32 application". When i asked what was meant by that, the answer was "a desktop application". This however makes little sense to me. FAT32 is a file system such as NTFS. Wouldn't it make more sense to say "NTFS application" due to the popularity of NTFS compared to the old and deprecated FAT32 ?
The term Fat client refers to a desktop application usually written as a native application for the user's platform.
"FAT32 application" doesn't make sense. As you say, FAT32 is a filesystem. However, "Win32" refers to a 32-bit Windows application (which is a common implementation choice for a fat client on Windows). I suspect the speaker might have conflated "Fat client" and "Win32 application" into "FAT32 application", which doesn't make sense. Either that, or the speaker actually said "Fat Win32 application".