For many of us, who are just end users, it probably doesn't matter that Google and Apple take arguably different approaches to how applications execute in the cloud and on the device. Developers, architects and geeks think it is more important.
At a high level, some might summarize the difference as Google viewing matters as "cloud and web." For Apple, cloud computing means "cloud and software."
All of the cloud computing services Google offers to consumers, like email, word processing and spreadsheets, happen within the browser. To Google, the point of cloud computing is to replace desktop software with the web. Apple is said to prefer execution within an app.
And of course, many will argue that there are many nuances. Some might say that Google tends to work with the browser are the frame, while Apple tends to work with the screen as the frame, for example. We dumb end users might have our own preferences. But I suspect most end users will appreciate elements of both approaches.