We are pretty far off the original question, but, yeah, there is a distinction. The fine structure constant is indeed more fundamental than the speed of light. How do you change the speed of light and not much else? You have to change at least the fine structure constant (in the IR limit, as you point out) and probably the gravitational coupling strength, and possibly some other free parameters in the standard model, like masses of the electron and quarks (again, in some dimensionless units). Otherwise something will go wrong with the Universe, the common example being carbon not being synthesized by stars. But I agree, these "side effects" of changing the speed of light may not have been important long time ago, or maybe in the galaxy far far away.