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.
CARD, BATTERY, LAWYER, and RHINO all fit the category "Things that charge". Charge has a different meaning for each. 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
PIXEL / ATOM / BYTE / SEED
PIXEL, ATOM, BYTE, 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.
Category
River words
DELTA / BANK / CURRENT / RAPIDS
DELTA, BANK, CURRENT, and RAPIDS 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
Hidden numbers
TENSION / HEIGHT / FREIGHT / STONE
TENSION, HEIGHT, FREIGHT, and STONE all fit the category "Hidden numbers". Each word hides a number sound or spelling. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.