Distortion is the lens moving points from where a perfect pinhole would have put them. Barrel pushes the edges out. Pincushion pulls them in. TV distortion is one number that summarises that error the way lens makers like to write it. It is not a full map, and it is not "the FOV."

In one sentence. Distortion bends the grid. Some applications can live with it. Metrology and "the aisle is 1.2 m wide" cannot.
TV distortion versus what you see
TV distortion compares the real image height at the edge with an ideal rectilinear height. A few percent is common on wide M12 glass. A fisheye will blow that definition up, because it is not trying to be rectilinear. Do not rank a fisheye on TV distortion and call it a bad rectilinear lens.
When it matters
- You measure. Robot pick, gap, fill level, occupancy of a bay.
- You stitch or stereo. Calibration can eat some of it. It cannot eat a sloppy spec you never measured.
- You read a code near the edge. The module still works, the quiet zone does not.
A doorbell can look a bit bowed. A dimensioning tunnel cannot.
The tiled-floor test
Stand at the end of a tiled corridor. If the grout lines belly, that is barrel. Your eye forgives it because you know floors are flat. A pixel-to-millimetre conversion does not know. Either you undistort with a real calibration, or you pick a longer, slower, more honest lens and take the narrower view.
How to read the library
Camemaker lenses filter TV Distortion (%). Use it inside one projection family. Then decide whether your software will calibrate. A low number on a rectilinear M12 is a gift. A high number on a fisheye is often the design.