There are a lot of differences from that to the Chao Garden of the Adventure games.
A second evolution, however, is more about a Chao changing form naturally instead of turning to a cocoon, indicating it aging throughout the 'years'.
A first evolution is when a Chao grows to an adult after around 4 hours of lifetime in the Garden. Like in the previous Chao Garden, a Chao has a first evolution and a second evolution. If they're unhappy, they die at their last year and will never be seen again. The main objective of the game is to raise your Chao and make sure they stay happy from life to rebirth. The gameplay of Chao World is heavily inspired by the Chao Garden of Sonic Adventure 1 and 2.