Before using a rectilinear lens, photographers should know its FOV but, because the FOV only depends of the focal length, they usually just ask for its focal length. For normal and tele lens this works very well but the wider the FOV the more they rather should ask for the FOV...
Before using a fisheye, photographers must ask for both the radius of the image circle and for the corresponding FOV (see important note.) When the image circle diameter is larger than the sensor diagonal, horizontal FOV, vertical FOV and diagonal FOV are usefull characteristics ...
Photographers must also ask for the mapping function of the fisheye lens, too. There is more than one type of fisheye. A rectilinear lens is just a wide angle lens with a different mapping function (known as "gnomonical"). Choices in fisheye lenses include "equidistant" (what I described in an earlier post before I found all these variations, which keeps distances the same), "orthographic" (gives the appearance of looking at an orb), "equisolid" (keeps areas the same, instead of distances), and "stereographic" (I'm not exactly sure I understand this one).
Important note: APP knows fisheyes focal length and camera sensor size but often fails (or don't attempt?) to place the image circle. Here is an example:
It will also need to know the mapping function of the lens in order to know how to simply correct it's geometry, if that differs from the intended geometry produced by stitching (which itself could be any of these mapping functions, including gnomonical for FOV well less than 180 degrees). My goal is to select a lens that has a mapping function equal to the mapping function of the panorama that is intended to be produced. I believe that would be the equidistant one. Apparently, a number of fisheye lenses are of the equisolid type, instead.
These mapping functions are similar in issue to what map makers have to deal with. For a map of a town, that is like a telephoto lens and the differences are too small to notice. For a map of a continent or larger, the differences are substantial.