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.
SCALE, LEGEND, COMPASS, and BORDER 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
River words
RAPIDS / BANK / CURRENT / DELTA
RAPIDS, BANK, CURRENT, and DELTA 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
Things with crowns
TOOTH / WATCH / TREE / KING
TOOTH, WATCH, TREE, and KING all fit the category "Things with crowns". A crown can sit on each of these. 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
FREIGHT / STONE / TENSION / HEIGHT
FREIGHT, STONE, TENSION, and HEIGHT 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.