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Themes change the way your Xoops site looks. They are usually provided in a compressed format (typically .zip). You just decompress this file and then copy the theme folder into the Xoops 'themes' folder. The new theme should then be selectable in 'Preferences Main/General Settings'.
Templates are 'Smarty' .html templates used to present data from modules. Each module installs a set of templates for each of it's pages and blocks. If you want to edit these templates online in the Xoops Templates Set Manager, you need to clone the default template set and edit the cloned files.
If you move site, you can download the cloned template set (Xoops automatically saves it as a tar.gz file) and then upload it to the new site.
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