In Pokémon Red and Blue you travel the land getting all eight gym badges. Once you have the badges, you take on the elite four. After you defeat the elite four, it is revealed that your rival (Blue) has become Pokémon champion right under your nose. You challenge your rival one last time and become a pokemon master.
In Gold and Silver, you see Kanto three years after the events in Red and Blue. You take on the 8 gyms of the region (Koga is replaced with his daughter Janine and Giovanni is replaced with Blue) and head up to Mt.Silver and fight Red (the player from Red and Blue.)
In Pokémon Red, Pokémon Blue, and Pokémon Yellow, the player's adventure is strictly limited to Kanto.
In Pokémon Fire Red, and Pokémon Leaf Green, the player has access to Kanto in addition to the Sevii Islands.