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.
LAUNDRY, LETTER, ORIGAMI, and MAP all fit the category "Things you fold". A crease is part of the process. 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
BYTE / SEED / ATOM / PIXEL
BYTE, SEED, ATOM, 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
Things with bars
CHOCOLATE / MUSIC / SOAP / SIGNAL
CHOCOLATE, MUSIC, SOAP, and SIGNAL 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
Airport words
RUNWAY / LUGGAGE / BOARDING / GATE
RUNWAY, LUGGAGE, BOARDING, and GATE all fit the category "Airport words". Travel days are full of these. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.