I learned about them as a construction worker while prepping process pipe for welds on oil refineries. Both tools are standards in the steam fitting trade. I’ve since used them on robot creations, blacksmith projects, and anywhere else metal is involved.
Flap disks are more forgiving than standard composite grinding disks. (Use grinding disks and stones to grind, but use the flap attachments to finish.) Flap disks allow the user to treat a work piece like a sculptor. There’s a sense of touch and shaping involved. Less likely to gouge while still smoothing at a fast rate.
The flapper wheel has similar qualities but gets inside tight spots and is excellent on irregular surfaces. Attach it to an end grinder, drill, or set one up on a bench grinder.
Here are before-and-after photos of a railroad spike knife that was ground with a flap-disk. (Actually it is the un-ground side of the knife vs. the ground side). Doing this took less than 2 minutes. — Aaron Nipper
Flap Wheels and Flap Disks: Around $10