I agree, to "burnish" lays down fibers of things like wood, ivory, fingernails, leather, etc. Can see a technicality in GIF example, the glass brush is nearly abrasive, more so to oxidation than parent metal.
Harder materials, the effect is slightly different but comparable result. The classic steel burnish is made removing teeth from fine cut files. Gunsmiths use those on lock work. The sides of a Swiss slitting file are tooth free, and work well.
Most butcher steels are almost burnishing tools, some have a very fine lengthwise pattern of grinding. Unsure if those have a different name; mine came from Grandfather. One glass smooth, the other grained, made ~100 years ago.
A pastime for infantry troops, used toothbrush handle on wood portions (stock) of their rifle, to brighten the sheen. Also known as 'boning'. Many different crafts use similar devices too, seamstresses, cobblers and bookbinders come to mind, though reasons differ.