How can two lenses with the same focal length have different viewing angles?
Q: How can two lenses have the same focal lengths, but a different viewing angle?
A: When you put the focal length in a formula to determine the viewing angle, the result you get is for a (non existent) "perfect" lens. It assumes, that the lens has no distortion, say, every pixel is found at the place where it should be for geometrical/mathematical reasons.
"real" lenses have distortion however, sometimes smaller sometimes bigger. If a lens has a negative distortion of say 10%,means it's image corners are 10% closer to the image center than expected. In the actual image corners is additional image information that shouldn't be visible.
If you check the diagonal viewing angle of such a lens, it is much bigger than calculated.
Lenses with lower distortion are expected to have an actual viewing angle that's close (or identical) to the calculated value.