The difference is in the behavior when you click on an internal link in the right half of the view (showing the tiddler you've navigated to). The internal version changes the right half of the view to show the tiddler you navigated to (navigation “internal” to the view), whereas the external version opens the tiddler you navigated to as a new item in the story river.

The behavior when navigating to other items that are listed in the table of contents (in the left half of the view) is identical for both versions.