Say an ordinary lens,
Sigma 30mm f1.4 for example, is designed for APS-C and thus produces images that have a 35mm-equivalence of 48mm.
But what about the fisheye lens?
From Wikipedia, it is said that for fisheye lenses:
The focal length is determined by the angular coverage, the specific mapping function used, and the required dimensions of the final image.
Also in the article, it is stated that a Circular, Stereographic fisheye lens that has a 4.2mm focal length for APS-C would be 6mm for a full-frame sensor.
So, what does the focal length mean for a fisheye lens? Does it have anything to do with the distance from the optical center to the sensor, or is it only a reference to the field of view this lens can provide assuming full sensor coverage?
Edit: As pointed out in the comment, the optical center is not the determinant for focal length. I guess a better-phrased question would be "Does the focal length on a fisheye lens have anything to do with its rectilinear counterpart?"