The wood boxes are two types of box that contain a trophy ornament.
If a Pokémon earned as a reward for clearing the Gym Leader Castle in Pokémon Stadium is traded to a Generation II game, that Pokémon will be holding one of the two wood boxes. A Pokémon earned in Round 1 will be carrying a Normal Box, which contains a Silver Trophy; a Pokémon earned in Round 2 will be carrying a Gorgeous Box, which contains a Gold Trophy.