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.
MUSIC, SIGNAL, CHOCOLATE, and SOAP all fit the category "Things with bars". Bars can describe 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
Kitchen verbs
DICE / WHISK / SEAR / FOLD
DICE, WHISK, SEAR, and FOLD all fit the category "Kitchen verbs". These are actions from a recipe. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Words before board
SCORE / KEY / DASH / SURF
SCORE, KEY, 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
Things with keys
MAP / LOCK / PIANO / HOTEL
MAP, LOCK, PIANO, and HOTEL all fit the category "Things with keys". Each one can be associated with keys. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.