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.
SEED, BYTE, 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 strings
KITE / VIOLIN / PUPPET / HOODIE
KITE, VIOLIN, PUPPET, and HOODIE all fit the category "Things with strings". A string is part of the object or how it works. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Spicy things
PEPPER / WASABI / CHILI / GINGER
PEPPER, WASABI, CHILI, and GINGER all fit the category "Spicy things". They can wake up your taste buds. 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
SIGNAL / SOAP / CHOCOLATE / MUSIC
SIGNAL, SOAP, CHOCOLATE, and MUSIC 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.