Biophysics vs. Biological Physics

I’ve wondered before if there’s any substantial difference between the terms “biological physics” and “biophysics”, because it seems that they’re sometimes used interchangeably. Then reading back over Ross’s condensed concepts post on July 22, I noted he had made a distinction between the two terms so I thought a bit of clarification early on would be a good idea. The best I’ve come up with is this:
Biophysics = existing physics applied to biological problems. We know the physics and we know the biological entities involved. Eg. action potentials in neuron firing.
Biological physics = developing new physical models relevant to biology. We might use existing physics concepts / approaches, but come up with descriptions that are “new” at least insofar as they are different qualitatively from existing models. Eg. ion channels?
Does this sound reasonable to you? Is there an example of biological physics that is more clearly different from biophysics? Does it matter?

This second definition sounds a little like the description Nelson gave in 1.3 of how physicists and biologists can best work together: as well as using powerful existing experimental and theoretical tools from physics to explore biology (eg. X-ray diffraction and…the maths used to describe co-operative helix-coil transitions in DNA), physicists can apply their knack for simplifying things to deduce new nontrivial, testable and relevant (!) hypotheses from simple accurate models of biological situations.
As a physics student with little background in biology, it’s been interesting to read chapter 2 this week while keeping in mind that a number of great “solutions” to problems in biological physics have, in the end, looked a lot like straight biology. That is, solutions have ended in suggesting the existence of new biological entities (some of which were among the different supramolecular complexes considered in ch. 2!!) such as ion pumps.