I am asking this question just for information and to clear my concepts about images in iOS
application (Retina
and non-retina
devices
The reason as to why we have to provide 2 images is because there are still people running the early devices that do not support retina display. They are lacking in the pixel amount as people running the retina, so we provide the normal amount. The thing with the iphone 5 requiring the @2x in the image file is because the @2x filename is the standard convention dealing with the retina display images.
That is why when you asked why don't we just put the 200x200 image in the 100x100 button. Well, if you're running a retina device, the image in that button will look like what you drew; however, if you're running something like a 3gs, that has no retina, then your image in that button will most likely come out to be pretty blocky, or blurry as the pixels are not matching the device's ratio.
Hope that helps clear anything up!