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.
KEY, DASH, SURF, and SCORE all fit the category "Words before board". Put one word after each answer. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Garden tools
RAKE / HOSE / TROWEL / SPADE
RAKE, HOSE, TROWEL, and SPADE all fit the category "Garden tools". These live in a shed. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Book parts
CHAPTER / COVER / SPINE / INDEX
CHAPTER, COVER, SPINE, and INDEX all fit the category "Book parts". They help make up a printed book. 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
CACTUS / MIRAGE / OASIS / DUNE
CACTUS, MIRAGE, OASIS, and DUNE 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.