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.
HOTEL, PIANO, LOCK, and MAP all fit the category "Things with keys". Each one can be associated with keys. 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 lanes
TRACK / ROAD / POOL / BOWLING
TRACK, ROAD, POOL, and BOWLING all fit the category "Things with lanes". Movement is organized into lanes. 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
CASHIER / PHONE / BELL / ALARM
CASHIER, PHONE, BELL, 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
Words after moon
LIGHT / BEAM / STONE / WALK
LIGHT, BEAM, STONE, and WALK all fit the category "Words after moon". Put one word before each answer. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.