If I have created a separate Photoshop and Element version of a product then, the Elements version of all the templates can be used in Photoshop and Elements. However, the Photoshop version cannot be used in Elements.
Photoshop is a more robust program offering more features and layer FX. Also Photoshop gives the option to organize layers in folders. Since Elements does not have the option for Folders, when you open the a template with Folders in Elements you cannot get to the layers in the folders and that's what causes most of the problems. In the case where the description says it will work with Photoshop or Elements, that usually means that it has no Folders or special FX that Elements cannot handle.
If you want to use the templates in Photoshop or Elements then I recommend that you buy the Elements version of the template.
If you upgrade to Photoshop, you can send me a support ticket asking for the new version and I can send it to you.