In simple words please, what is the "Rendered file" image-format?
Since Drupal 7 Images can be rendered the same way as any other entity. Images are a special case of a file and file is a fieldable entity.

Fields can be added to the entity and how the fields are displayed can be configured here:

admin/structure/file-types/manage/image/display

But most times you don't want a rendered file, but a resized image. That is provided by the module "image" in core and if enabled you can configure image styles and use this in node displays and views.