[Brightcolours]

I already wrote "(or angle of view, more precisely)".

 

Then, if the labeled 12mm FL for the wide end of the 12-40mm lens is the true FL at the wide end, then after the distortion correction the diagonal view angle of the image would be that of FL like 13mm?

No, it will be 12mm. Like I said, uncorrected lenses or under corrected lenses give a wider view for the same focal length. So what you end up with a similar view as any other well corrected 12mm lens, after correction of the barrel distortion.

The native distortion at 12mm is very large, about 8% according to the test. On the other hand, it seems that the labeled FL at the two ends of a zoom lens is often not quite accurate.

 

My Nikor 16-35mm also has a high distortion at 16mm, about 5% I guess. Each time after I correct the distortion afterwards I clearly see the change in angle of view which I don't like. So I only correct the distortion when it is necessary.

Same story. The 16-35mm you have is not well corrected at 16mm, and gives a wider view than a better corrected lens at 16mm. When you correct the barrel distortion, you end up with a similar width as with the well corrected lens.