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.
DICE, SEAR, WHISK, 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
Things that fly
JET / EAGLE / KITE / DRONE
JET, EAGLE, KITE, and DRONE all fit the category "Things that fly". They spend time in the air. 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
ATOM / BYTE / SEED / PIXEL
ATOM, BYTE, SEED, and PIXEL 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
Mystery story clues
EVIDENCE / ALIBI / MOTIVE / SUSPECT
EVIDENCE, ALIBI, MOTIVE, and SUSPECT all fit the category "Mystery story clues". A detective asks about these. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.