The taxonomy module makes it possible to associate terms to all the content of the site and thus to classify and organize this content. It is then possible, with the help of additional modules, to use these keywords / tags for different functionalities: multicriterion searches, organization of navigation menus, access control, etc.
A template is a reference, from which all pages of the site are created and integrated. The Drupal templates, called Themes, give the site the desired overall appearance.
The theme is a collection of files and images that make up the design (layout, colors, etc.) of a Drupal site.
Twig is a PHP template engine built into Symfony 2 and Drupal 8 with the advantage of separating the presentation layer in dedicated templates for better maintainability of the code. Twig makes it possible to manage the inheritance between the template and the layout. Thanks to this template engine, the syntax is cleaner and reusable and the HTML code is more readable.