Can I play Vive and Rift game on 3rd party PC VR headsets?

I have a question about virtual reality headsets for the PC. I wanted to know what is the difference between all the hundreds of VR headset for PC compared to the popular ones (e.g. HTC Vive, Oculus Rift) and the ones coming from Microsoft for Windows 10. I am not talking about mobile VR, only those who are for the PC/Windows.

I am also interested to know if I can play vive and rift games on those headsets, and if not, what games are compatible with those, certainly not Android, so which experiences?