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.
TIMER, WATCH, CLOCK, and HOURGLASS 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.
Category
Hidden numbers
STONE / HEIGHT / TENSION / FREIGHT
STONE, HEIGHT, TENSION, 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
Map features
BORDER / COMPASS / LEGEND / SCALE
BORDER, COMPASS, LEGEND, and SCALE all fit the category "Map features". These help you read a map. 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 / FROST / SLED / PARKA
ICICLE, FROST, SLED, 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.