Native file management plugins of editor libraries
The Wysiwyg module does not support the native file management plugins of any editor.
That is, because Drupal core has a built-in file API to record and store "managed" file records; i.e., the system knows and keeps track of files that have been uploaded (through any module) by a user, as well as how often and where a file is used. Furthermore, user access permissions to individual files need to be taken into account, too. And lastly, it is technically possible to "share" managed files between modules; i.e., to re-use them in different scenarios, or for different content. An editor's native file manager would circumvent all of this internal logic.
Instead, there are a couple of contributed Drupal modules that integrate with Wysiwyg module to expose a so called "Drupal plugin" that works in all editors that support Drupal plugins. These plugins basically use Drupal's native file handling support to upload and manage files (typically in an own/custom dialog). If an editor provides means to expose "Browse" buttons wherever files/URLs/etc could be selected by an end-user, then those plugins additionally try to adjust the editor configuration so that the "Browse" buttons are opening the module's file browser and return the result to the editor's editing widget.
A (poor) example for this is http://drupal.org/project/imce_wysiwyg. Another example could be http://drupal.org/project/media, but as of now, Media module does not attempt to integrate with an editor's native widgets for linking to/embedding files/URLs/etc.