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.
MOSS, LIME, FERN, and PEA all fit the category "Green things". They commonly show up in green. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Card suits and kin
CLUB / SPADE / HEART / DIAMOND
CLUB, SPADE, HEART, and DIAMOND all fit the category "Card suits and kin". A deck has all four. 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
Timekeepers
HOURGLASS / CLOCK / WATCH / TIMER
HOURGLASS, CLOCK, WATCH, and TIMER all fit the category "Timekeepers". They help measure time. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.