The answer to that long and unwieldy sentence is 'it depends'. Actually, depends on the exact projection equation used in the optical design.
Ignoring any near range differences, an 8 mm lens on-axis will yield the same magnification of detail, but not necessarily the same field of view. Looking at this in reverse, the same field of coverage might be produced by lenses with different focal lengths. For example, my 8 mm f/2.8 and 10 mm f/5.6 fisheye-nikkors both cover 180 degrees, but the manner in which this coverage is manifested will be different. See the examples below.