Formatters are used to turn the raw data for a single field value into html. The Display Fields tab lets you chose which formatter you want to use for each of your fields.
In CCK 2.0 for Drupal 6, all formatters now go through the theme layer. Therefore, overriding a formatter's theme is another way you can alter how your values are displayed (whereas changing content-field.tpl.php lets you change the html that "wraps" the values).
Most formatters come as theme functions, but some might use templates instead. Either way, you can override them using the usual Drupal 6 theme override practices. For more informations, see the Theme guide for Drupal 6, and more specifically the Overriding themable output section.