What is the difference? I think it's easiest to understand by thinking of a free-text search query as causing you to be dropped at some arbitrary point on a map. Our planet is sparsely populated, as pictured below, so most of the area of the map is off-road. Hence, if you're dropped somewhere at random, you're really in the middle of nowhere. Before you start trying to find nearby towns and attractions, your first task is to find a road.
How does this metaphor relate to clarification vs. refinement? Clarification is the process of finding the road, while refinement leverages the network of relationships in your content (i.e., the network of roads connecting towns and cities) to enable navigation and exploration.
"Did you mean..." is the prototypical example of clarification, while faceted navigation is the prototypical example of refinement. But it is important not to confuse the concrete user interfaces with their intentions. The key point, on which I'm glad to see Peter agrees, is that clarification, when needed, is a prerequisite for refinement, since it gets the user and the system on the same page. Refinement then allows the user to fully exploit the relationships in the data.