How can one move the position of the application inside the launcher?
It looks like you are using TouchWiz.  If so, go to the App Drawer (Picture B).  

The directions below will vary slightly based on the version of TouchWiz you are running.  

Hit the Menu Button, and select View Type, then select Customizable Grid.  

Then, hit the Menu button again, and select Edit.  In this view, you can move your icons in the App Drawer.  

For what it's worth, you can also edit your dock icons.