From Bulbapedia, the community-driven Pokémon encyclopedia.
Toy Pokémon (Japanese: グッズ ポケモン Pokémon toy) are miniature wind-up toys that resemble Pokémon, and are the only type of Pokémon that appear in Pokémon Rumble and Pokémon Rumble Blast. There are currently 717 different Toy Pokémon.
Toy Pokémon behave much like normal Pokémon do. They are generally friendly, and all share a common love for battling and teamwork. In order to operate, a Toy Pokémon must have a working Wonder Key which provides them with life. Otherwise, they are lifeless toys. Over time a Toy Pokémon may become Rusty, or they may become Rusty after coming in contact with Dark Rust. A Rusty Toy Pokémon will only be able to perform the move Struggle, or otherwise be controlled by Dark Rust if they are completely consumed by rust. Rusty Toy Pokémon will need to be cleansed with Glowdrops to be restored to normal.
Differences between Toy Pokémon and normal Pokémon
Toy Pokémon can only know two moves at a time as opposed to the usual four. Also, instead of having Abilities, Toy Pokémon may have Special Traits. Toy Pokémon cannot grow or evolve like regular Pokémon, and retain their Power level and stats their entire lives. In order to gain an evolution, the player must release a number of the same species to be given a Special Ticket for the next stage of evolution (Pokémon Rumble), or simply be given the evolution in exchange for the previous stage (Pokémon Rumble Blast).
A Toy Pokémon has five set statistics as opposed to the usual six: HP, Power, Attack, Defense, and Speed. Each species of Toy Pokémon has a set base Attack, Defense, and Speed, and each individual Toy Pokémon has a Power level that determines how much damage a move will do. Toy Pokémon with higher Power levels can be found later in the game, or when the World Rank is increased after completing the game.
Shiny Toy Pokémon
Like normal Pokémon, a player has a very slim chance of finding a Shiny Toy Pokémon in Pokémon Rumble. However, when playing with multiple players, the odds of finding a Shiny Toy Pokémon greatly increase to the point that it would be unlikely not to find one or two while playing.
Shiny Pokémon have been removed from Pokémon Rumble Blast.