As far as I remember from a previous project from a few years ago, the browser doesn't include a referrer for the download request, which can be used for a distinction. (You'll have to disable caching and E-Tags for this to work.)

However, this is easily defeated by the use of the console: Select the sources tab, locate the image and simply drag-and-drop the image from there, which will use the local cache instance for the source. Works also with this site, at least with Safari.