The only difference is Apple makes their own operating system and includes it when you purchase one of their PCs. Nearly every other brand of PC besides Apple includes a third-party operating system. Some PCs are sold without an OS too.
"Macintosh" or "Mac" is simply a marketing name for Apple computers just as "XPS" is a marketing name for Dell computers. But "Mac OS" also refers to the operating system such as Mac OS X. Saying just "Mac" would be talking about the line of personal computers (PCs) produced by Apple, Inc. that just happen to come with a different OS then most other PCs on the market.
The clearest, and most concise answer yet, I must commend you for it.
Mussels is right, they are probably going to be opening themselves up to a world of pain if they allow any man and his dog install OS X on a regular computer.
If IBM had hurried up development and production of their dual-core 3GHz PPC G5s, we would more than likely still be seeing Apple using PowerPC architecture, which would have meant less trouble for Apple.
Hell, my G3 clamshell could emulate Win 98 at a decent speed, even running VB6, and having relatively low compile times to boot, so if they had continued with the PPC achitecture, it wouldn't have detracted much from Apple hardware, but they might have also had to come up with a G6 or something similar to combat the Core architecture, which has Intel back as the performance king again.
VroomBang, anybody with a thirst for challenge, with an inquisitive mind, might just want a *nix OS, which could include either PC or Mac. Fine, you can't OC a Mac, but once you've started figuring out how to build your own distro, most people likely ignore that, so it's platform-independant.