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, SCORE, DASH, 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
Baking staples
SUGAR / YEAST / BUTTER / FLOUR
SUGAR, YEAST, BUTTER, and FLOUR all fit the category "Baking staples". A bakery keeps these close. 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
DIAMOND / CLUB / HEART / SPADE
DIAMOND, CLUB, HEART, 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
Desk items
LAMP / STAPLER / NOTEBOOK / PENCIL
LAMP, STAPLER, NOTEBOOK, and PENCIL all fit the category "Desk items". They belong within arm's reach at work. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.