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.
TREE, KING, WATCH, and TOOTH 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
Things that ring
PHONE / CASHIER / ALARM / BELL
PHONE, CASHIER, ALARM, and BELL 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
Things with keys
MAP / LOCK / PIANO / HOTEL
MAP, LOCK, PIANO, and HOTEL 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
Spicy things
PEPPER / GINGER / CHILI / WASABI
PEPPER, GINGER, CHILI, and WASABI all fit the category "Spicy things". They can wake up your taste buds. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.