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, MAP, LETTER, and ORIGAMI 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
Things with lanes
BOWLING / TRACK / POOL / ROAD
BOWLING, TRACK, POOL, and ROAD all fit the category "Things with lanes". Movement is organized into lanes. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
River words
DELTA / BANK / RAPIDS / CURRENT
DELTA, BANK, RAPIDS, and CURRENT all fit the category "River words". Fresh water flows through this set. 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 / PIXEL / SEED
ATOM, BYTE, PIXEL, and SEED 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.