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.
FALCON, ARROW, COMET, and SPRINTER all fit the category "Fast things". Speed is the common thread. 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
DIAMOND / SPADE / HEART / CLUB
DIAMOND, SPADE, HEART, and CLUB 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
Things that charge
RHINO / CARD / BATTERY / LAWYER
RHINO, CARD, BATTERY, and LAWYER 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
River words
DELTA / RAPIDS / CURRENT / BANK
DELTA, RAPIDS, CURRENT, and BANK 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.