From the Super Mario Wiki
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They can be forced open by any attack and reveal their contents upon doing so. As their wooden appearance compared to their metal counterparts indicates, rather than containing one of Wario's Treasures, Wooden Chests contain more common items like Garlic, a Smiley Bomb, or Coins. When Wario re-enters a Wooden or a Steel Trapdoor after having completed the minigame inside, he finds a Wooden Chest where the Red Diamond used to be.