Pokemon Green is the Japanese version of the North American version, Pokemon Blue. The only difference between Pokemon Red and Pokemon Green (or Blue) is the Pokemon. Pokemon Red has Electabuzz while Pokemon Green (or Blue) has Magmar. But there are other version exclusive Pokemon, as well. In 2004, Nintendo made a handheld remake of both Pokemon Red and Green (or Blue). It was called Pokemon LeafGreen and Pokemon FireRed.
The objective of the game is to catch all the Pokemon in the Kanto region and collect all the 8 Gym Badges and become the Elite Four Champion. The game takes place in the Kanto Region where a boy or girl accidentally is about to step in grass when Professor Oak stops them and gives them a Pokemon. They have 3 choices: Bulbasaur, Charmander, Squirtle. Then, their childhood rival comes and chooses a Pokemon, as well. They will choose the Pokemon that is strong against your Starter's type. When you leave the lab, your rival will challenge you to a battle. If you win, your Pokemon will get experience points and you will win money. From then on, you have to complete the Pokedex and win all the eight Gym Badges of Kanto. The eight Gym Badges are from different cities, different Gym Leaders, etc. A Gym Leader specializes in a certain type like Brock of Pewter City specializes in Rock-Type Pokemon. There are also some bumps on the road, too. An evil group called Team Rocket who tries to take people's Pokemon and try to stop you and whatnot. Ironically, the Team Rocket boss Giovanni is the last Gym Leader. He specializes in Ground types.