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.
DUNE, CACTUS, MIRAGE, and OASIS all fit the category "Desert words". Think sand and heat. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Fast things
FALCON / SPRINTER / ARROW / COMET
FALCON, SPRINTER, ARROW, and COMET 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
Things that bloom
ALGAE / TULIP / FIREWORK / ROSE
ALGAE, TULIP, FIREWORK, 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
Map features
LEGEND / BORDER / COMPASS / SCALE
LEGEND, BORDER, COMPASS, 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.