The first hallmark of the Second Wood Box Edition from Gentosha and Pieco is the corrugated cardboard outer sleeve, and shrinkwrap outside that. The sleeve features friendly graphics, pretty perspicuously designed to draw children to it on the shelf at a shop.
The First Edition wooden box is approximately a half-bottom, half-top box; the Second Edition has a thin platform-bottom, with full-height inside walls, and then the lid covers all the way down to the platform — i.e. 90% of the way to the table. The Second Edition box is made out of balsa or some similarly sparse would. Also, instead of featuring a chick and a chicken woodburned in the center of the lid, the Second Edition has the lion, and the name of the game (おおきな森の どうぶつしょうぎ) woodburned in the lid's center.
As with the First Edition, there is a cloth board, and the pieces are square blocks of wood — much smaller than those in Let's Catch the Lion! — with stickers on one or both sides, depicting the animals and their moves.
The Second Edition contains a 16-page (cover-to-cover, that is), pamphlet-sized book, which serves as an introduction to the game. It is specifically written for kids to read: It uses hiragana for even "shogi" (つしょうぎ), and slowly introduces kanji, with kana above it to help children learn the kanji (kanji for "shogi" is 将棋). This makes it so anyone can read basic hiragana can learn shogi, and upgrade from Let's Catch the Lion! (3×4 board with 8 animals) to Let's Catch the Lion in the Big Woods! (9×9 board with 40 animals), as the introduction explains.