Nintendo is a video game company.
The Pokémon Company is responsible for the marketing and licensing the Pokémon franchise.
Game Freak is a video game developer.
Basically, Game Freak makes the games for Nintendo (who also makes the devices, like 3DSes), and The Pokémon Company takes care of other stuff like Pokémon t-shirts and plushies.
Pokémon Company
Game Freak
Nintendo