Xbox is becoming the branding for entertainment. Kind of weird but that's where they're going with it because of the success that the Xbox has become. That's why there's Xbox Music.
You can't play Xbox 360 Games on the PC nor can you play Windows games on your 360.
You do have an Xbox gamerscore and that encompasses all your Xbox games, Games for Windows, and Windows 8 games. I remember way back when I saw a friend playing Angry Birds and I was thinking, "there's Angry Birds on the 360???". But he was playing it on his phone. Now there's an Angry Birds for the 360 but it's a compilation with upgraded graphics but it's really expensive.
And you can check what your Xbox friends are doing while on your PC. You can use your Windows 8 PC (or Windows Phone or Android or iOS device) with your Xbox 360 as a SmartGlass device. Functionality ranges from using the SmartGlass device as a remote control for the Xbox, using your smartphone/notebook's keyboard as your 360 keyboard or for added functionality like using the second monitor as a GPS screen for Forza Horizon (a racing game). Like in the karaoke game for the 360, while someone is singing, people could be choosing songs and adding them to the playlist from their smartphone. That way, there's no sitting around while your friend is choosing songs like in a traditional karaoke scenario. You're just jumping from one song to the next with no dead time.
And there's potential for interactivity between an Xbox 360 game and a Windows 8 game (for example, imagine playing poker with one person on his 360 and another person on his Windows 8 PC), but right now, the interactivity is very limited.