Filtered HTML Text format without an editor
First you create your two text formats (if not already present).

Then you can use the wysiwyg module (http://drupal.org/project/wysiwyg) to display an editor for the Full HTML text format (on /admin/config/content/wysiwyg). wysiwyg will only display editors that you have set up properly (usually by placing a third party library in sites/all/libraries)

You can limit use of the text formats via the permission settings.