This recipe uses many variable name action hooks to register functions to be called when users create or modify book types in the taxonomy editor. The first two calls to add_action refer to the <taxonomy>_edit_forms_fields and <taxonomy>_add_form_fields hooks. While you might expect to see two different functions associated with each of these action hooks, we actually register the same function in both cases, since rendering an additional field is similar in both cases. That being said, part of the function we register checks to see whether it receives a valid object as a parameter to know how it should render the new field so that it fits on the page if the user is creating a new category or editing an existing one.
We use a similar technique with the edited_<taxonomy> and created_<taxonomy> action hooks, which are respectively called when you first save a new taxonomy and update an existing one. In this case, the code does not have any significant differences depending on the action, since we only need to validate and save the incoming value for the new field.