Not talking about all the Linux distros or different versions of Windows obviously. And my definition of “desktop” would be “able to connect to WiFi and launch a modern web browser”, since that would cover 90% of most people’s use cases.
I know of:
Windows
MacOS
GNU/Linux
GNU/Hurd
BSD
HaikuOS
What others are there?
Android is Linux. iPhone is iOS/MacOS. So I think those are covered depending on how you define “family”
In this context, I think two operating systems are in the same family if software for one can be recompiled for another with minimal changes without heavyweight compatibility libraries.
In that sense, I would put BSD and traditional desktop Linux distributions in the same family even though they don’t share low-level code, and I would exclude Android even though it uses the Linux kernel.