The full solution is below, with a short explanation for each group. To avoid spoilers, play the puzzle or open the hints page before reading the answer panels.
LENS, FLASH, FOCUS, and SHUTTER all fit the category "Photo terms". A camera owner knows these. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Soft things
VELVET / FLEECE / MIST / PILLOW
VELVET, FLEECE, MIST, and PILLOW all fit the category "Soft things". They suggest a gentle texture. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Tiny units
BYTE / SEED / PIXEL / ATOM
BYTE, SEED, PIXEL, and ATOM all fit the category "Tiny units". Smallness connects them. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Things in a gym
BENCH / MAT / KETTLEBELL / ROPE
BENCH, MAT, KETTLEBELL, and ROPE all fit the category "Things in a gym". Training rooms are their habitat. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.