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.
POOL, TRACK, ROAD, and BOWLING all fit the category "Things with lanes". Movement is organized into lanes. 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 / MIST / FLEECE / PILLOW
VELVET, MIST, FLEECE, 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
Card suits and kin
HEART / DIAMOND / CLUB / SPADE
HEART, DIAMOND, CLUB, and SPADE all fit the category "Card suits and kin". A deck has all four. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Photo terms
SHUTTER / LENS / FOCUS / FLASH
SHUTTER, LENS, FOCUS, and FLASH 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.