Obviously you have to trade to get the other...
But no they aren't the same game. Emerald has a different story, as Rayquaza is included in the story, and he isn't just and extra you find in Sky Tower. Rayquaza plays a big part in the storyline as he stops Groudon and Kyogre from kicking the crap out of eachother.
No they are not the same game.
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There are many Pokemon you catch that are similar in sapphire and emerald but there are many Pokemon emerald can only get and not sapphire.
ruby, sapphire, emerald, fire red, leaf green
You can't catch it in Pokemon Sapphire, Ruby, Emerald. The only way to obtain it is to buy it in the Game Corner for 9999 slot coins in Pokemon FireRed and LeafGreen and then trade it to your Ruby/Sapphire/Emerald game.
The only way to obtain Aerodactyl in Ruby, Sapphire, or Emerald is to trade it from another game.
Pokemon Emerald,Ruby and Sapphire