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.
SPRINTER, ARROW, COMET, and FALCON 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 ring
PHONE / BELL / CASHIER / ALARM
PHONE, BELL, CASHIER, and ALARM all fit the category "Things that ring". Each can make a ringing sound. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Airport words
LUGGAGE / GATE / BOARDING / RUNWAY
LUGGAGE, GATE, BOARDING, and RUNWAY all fit the category "Airport words". Travel days are full 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
Baking staples
SUGAR / YEAST / FLOUR / BUTTER
SUGAR, YEAST, FLOUR, and BUTTER all fit the category "Baking staples". A bakery keeps these close. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.