In order to upload, update, share or delete templates, the webpublisher_templatedesigner role is required.
Users with webpublisher_specdesigner role can add templates found in the Shared Templates Library to document specifications.

My Templates

The user Templates Library is a collection of templates stored on the server that belong to the user that is logged in. Each user has a different Templates Library.
A user can update, share and detele only templates from its own library.

Shared Templates Library

The Shared Templates Library is a collection of templates stored on the server that were shared by the user that is logged in or by other users.
The logged in user can not see other users’ templates, unless they are shared.