Pincers and nippers each fall under the category of tools, and farriers may well use both, as they may wish to trim a hoof or to pull a nail out.
To me, the distinction is that nippers cut and pincers grasp, though
in a pinch, I’ve used nippers to grasp and pincers to cut. In my view, nippers also have a smaller throat proportionately, than pincers.

Nippers (top) tend to be sharper and harder than pincers (bottom), so there is a danger of nipping off the thing you want to merely pinch. Contrariwise, pincers are more likely to tear or crush than to nip, and may be damaged with a notch if the object is hardened.

I associate Red Devil more with glazing and painting than ranching, so maybe the rounder jaws are for reaching into narrower spaces than the more oblong jaws I usually see.

I have more pincers (all above) than nippers.

I put yellow vinyl grips on my favorite pincers, and blue grips on my favorite nippers. My house is more than a century old, and held together with square cut nails, so these two have done a lot of sevice with renovations.