Avada Builder is in the WordPress backend; it is a block style page builder. Avada Live is in the WordPress front end; it is a visual builder.
For more detailed information go here: https://avada.com/documentation/avada-builder-vs-avada-live/
To add a template to a page click on the Library icon in the page editor, select the template you would like to add to the page.
To add an element you must have a container added to the page editor. Once you have a container click on the Library, then click on the Elements tab and select the saved library element you need