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.
MAP, HOTEL, PIANO, and LOCK 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
Desert words
DUNE / MIRAGE / CACTUS / OASIS
DUNE, MIRAGE, CACTUS, 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
Soft things
VELVET / MIST / PILLOW / FLEECE
VELVET, MIST, PILLOW, and FLEECE all fit the category "Soft things". They suggest a gentle texture. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Film crew roles
GAFFER / PRODUCER / EDITOR / DIRECTOR
GAFFER, PRODUCER, EDITOR, and DIRECTOR all fit the category "Film crew roles". They appear in movie credits. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.