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.
TENSION, STONE, HEIGHT, and FREIGHT 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.
Category
Garden tools
RAKE / TROWEL / HOSE / SPADE
RAKE, TROWEL, HOSE, and SPADE all fit the category "Garden tools". These live in a shed. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Winter words
ICICLE / SLED / FROST / PARKA
ICICLE, SLED, FROST, and PARKA all fit the category "Winter words". Cold weather brings these out. 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
RAPIDS / DELTA / BANK / CURRENT
RAPIDS, DELTA, BANK, 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.