Uninstalling versus disabling apps

When I select the menu entry called "Uninstall/Disable apps" - from the apps drawer which can be reached from any home screen by tapping the 16-square icon in the lower-right hand corner - I can disable or delete any apps. However, clicking on an app disables it. I remember being able to uninstall apps by dragging them to a delete trash can icon. I cannot figure out how to delete an app on the apps drawer. Also, while I realize this might vary from app to app, what would be some of the most common reasons/advantages to disabling an app? P.S. I think the screens accessible by clicking the 16-square icon are what is called the app drawer, correct me if I'm wrong. Thanks. I am on a Samsung Galaxy SIII (Android KitKat 4.4.2) and I am cussing the default TouchWiz launcher. (I would have liked to attach screenshots but at the moment my network connection is slow).