Actually that is very usefull.
When you ask a UIScreen for it’s Bounds you get the bounds of the screen, which is the whole device screen. (the status bar is part of the screen)
But if you ask a UIScreen to tell you where and how big can be the root view of your application asking for the applicationFrame is usefull.
There is no direct relationship between the 2 calls except that the applicationFrame is returned in the UIScreen bounds coordinate system. (But the status bar is not part of your application, that explain the different result)
applicationFrame
The frame rectangle to use for your application’s window. (read-only)
@property(nonatomic, readonly) CGRect applicationFrame
Discussion
This property contains the screen bounds minus the area occupied by the status bar, if it is visible. Using this property is the recommended way to retrieve your application’s initial window size. The rectangle is specified in points.