All that happens when you clone a template set, is that all the files which make up the template set you are cloning, are copied and renamed, to create an identical (clone) set of template files.
This cloned template set is then stored in the database template table, with an entry identifying the individual templates and their [/i]template set[/i], in the template set table.
No files are actually stored on your servers hard drive.
If you want to have a copy of the cloned template set, you need to click on the 'download' link, which will make a copy of the templates stored in the database, and save them as files into a zip folder with the name previously given to the template set.