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, COMPASS, BORDER, and LEGEND 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
Book parts
COVER / SPINE / CHAPTER / INDEX
COVER, SPINE, CHAPTER, and INDEX all fit the category "Book parts". They help make up a printed book. 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 bloom
ALGAE / FIREWORK / TULIP / ROSE
ALGAE, FIREWORK, TULIP, and ROSE all fit the category "Things that bloom". Each can bloom in its own way. 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 / FREIGHT / STONE / HEIGHT
TENSION, FREIGHT, STONE, 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.