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.
KEY, DASH, SCORE, and SURF all fit the category "Words before board". Put one word after each answer. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Ocean words
REEF / KELP / WAVE / TIDE
REEF, KELP, WAVE, and TIDE all fit the category "Ocean words". They belong near salt water. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Spicy things
GINGER / PEPPER / WASABI / CHILI
GINGER, PEPPER, WASABI, and CHILI all fit the category "Spicy things". They can wake up your taste buds. 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
SPADE / DIAMOND / CLUB / HEART
SPADE, DIAMOND, CLUB, and HEART 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.