The main menu is the menu that you start your file on.
Story Mode is a mode that allows you to go through levels and train your Pokémon. It is the main portion of gameplay.
Challenge Mode is a mode that allows you to complete certain challenges for rewards.
Multiplayer is a mode of PTD that was released in v5.1. The idea was first announced in a blog post on May 26. It was made clear that Single Player Mode would have the majority of Sam's creative attention. You connect with online players and play with Pokémon given to you.
Trading is another part of the game where you go to a different site to trade with other trainers.
The Pokédex is a new feature in PTD from version 2.8. It keeps track of Pokémon you've seen and achievements you've unlocked. You must save your PTD profile online to use this feature. A Pokédex is awarded after completion of Mt. Moon (Challenge Level).