Apple's approach is that OS X and iOS devices such as iPhone, iPod touch, iPad and Apple TV should feel the same but need not look the same. The divergence in these approaches can be seen as Microsoft keeps working toward putting touchscreens on PCs while Apple focuses instead on the touchpad, making sure that the touchpad experience is intuitive to consumers familiar with iOS.
While Windows 8 is still in prerelease form, Apple today has released the latest version of OS X, Mountain Lion, which shows just how Apple sees the role of the PC in a post-PC world. After using Mountain Lion for the last week, I would call it a relatively minor release with major additions to the operating system itself and subtle but important changes to the user interface. Those UI changes make OS X fit much more seamlessly into the ecosystem of Apple's platforms.
With Mountain Lion, integration with Apple's personal cloud services, known as iCloud, is much tighter. This emphasizes that the PC is just one device among many, while also suggesting that the personal cloud will drive long-term consumer adoption. For example, iOS devices are able to link to Apple TV, either to display content or to use the TV for interactive experiences such as games. Mountain Lion extends this to the Mac with AirPlay Mirroring, which allows content to flow from Apple device to Apple device, from screen to screen, and from location to location. The result? Apple TV not only makes an excellent vehicle for presenting and displaying content, but also a great gaming platform that allows a mixture of devices to become game consoles for multi-player, high-definition games.