Here's one way to look at it:
A sequence of view-controllers within single navigatoin controller represent a single workflow in user's head. If at some point you need to interrupt the current workflow and create a diverging workflow you create a modal dialog. If the new workflow only has one step you simply present corresponding controller, but if there are many steps you create a new navigation controller to string the steps together.
The visuals are different - with nav controller user's attention moves from left to right, while with modal dialog from top to bottom. Imagine that you are flipping a book (left-to-right) and at some point you move the book away from you and then pull another book from under the table and place it in front of you (top to bottom), and then start going through that another book (left-to-right). Then you close the whole second book and move back to first book where you left off.
The addSubview method is on a different abstraction plane - subviews are used to create the two experiences I described above. You can use subviews to create a different experience which would be on the same abstraction level. Couple more examples of the constructs on the same level are UIAlertView and UIActionSheet.