List saved as template does not appear under Add an app or what lists can you save as template and use for creating other lists based on them.
You are trying to achieve the following :
save a list as template, export the saved stp file and import it into a different environment to be able to create a new list based on this template.
however, after importing it successfully, you discover that the list template is not displayed among the available templates when you click "add an app" ( by the way, did I mention this applies to Sharepoint 2013?)
The explanation for the template not being displayed can be one of the following ( except invalid templates of course, but then you would get a full-blown error ) :
1. the language of the template is different than the language of the site where you want the template to be used.
2. the version of the template does not match the minimum version difference accepted by the site where you are attempting to use it ( ex. you are saving a Sharepoint 2007 list and are trying to use it in a Sharepoint 2013 environment)
3. the template is hidden by design
For point 3 you may ask yourself, why ?
Well, it makes perfect sense if you think about what list templates are hidden by design:
No Code Workflows
No Code Public Workflows
Persistent Storage List for MySite Published Feed
Custom Workflow Process
These lists once created in a source site have a strict dependency to the site and environment where they were created. So, even though you might be able to save them as template ( with content, even) using UI or OM, importing these lists templates in a separate environment would not make any sense and is bound to cause more issues that it would solve due as said to the strict dependencies to the original site.
BTW., the most common example would be saving a Tasks library in your Sharepoint 2010 and trying to use it in Office 365 or on Sharepoint 2013.That won't work.