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.
TIDE, KELP, WAVE, and REEF all fit the category "Ocean words". They belong near salt water. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Night sky
NEBULA / METEOR / VENUS / ORION
NEBULA, METEOR, VENUS, and ORION all fit the category "Night sky". Look up after sunset. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Fast things
ARROW / FALCON / COMET / SPRINTER
ARROW, FALCON, COMET, and SPRINTER 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
Board game pieces
TILE / PAWN / TOKEN / DIE
TILE, PAWN, TOKEN, and DIE all fit the category "Board game pieces". You might move or roll these on a tabletop. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.