There are two different terms here:
1. "Ajax request generates non-Ajax response" when the whole DOM tree is replaced
2 "Partial Navigation" when the only part of the page limited by a4j:include
The common part between those cases is action method returning the valid action outcome. Instead of replacing the parts of the current view, the context of target view is used for whole page replacing or partial page replacing.
Speaking about the tech details, the response come using the same channel. The "Ajax request generates non-Ajax response" mode (but not "Partial Update") requires < redirect /> declared for navigation rule to avoid memory leaks or object interferes.
If the navigation rule has < redirect /> declared, the true Non-Ajax response is processed.