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
Hidden numbers
FREIGHT / STONE / HEIGHT / TENSION
FREIGHT, STONE, HEIGHT, and TENSION all fit the category "Hidden numbers". Each word hides a number sound or spelling. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Weather events
HAIL / SQUALL / FOG / DRIZZLE
HAIL, SQUALL, FOG, and DRIZZLE all fit the category "Weather events". Forecasts warn you about these. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.
Category
Coffee shop orders
AMERICANO / MOCHA / CORTADO / LATTE
AMERICANO, MOCHA, CORTADO, and LATTE all fit the category "Coffee shop orders". You can hear these at a counter before 9 a.m. The shared link accounts for all four words, which is why the remaining board words should be tested against a different rule.