Although the other answer is technically correct it didn't really answer your question regarding Iris. But it is right in saying the Anime and the Games are two completely different things even if they do share several similarities.
Almost every question here can be answered with one simple answer.
THE ANIME, THE GAMES, AND THE MANGA ARE ALL DIFFERENT THINGS. - DT
In the Games:
Iris is the Gym Leader of the Opelucid City Gym in Pokémon White.
(Drayden is the Gym Leader in Pokémon Black and Pokémon Black and White 2.)
Iris is the Champion in Pokémon Black and White 2.
Iris is a Master Dragon-type Trainer. She was one of the Gym Leaders of Opelucid City's Gym, known officially as the Opelucid Gym, giving out the Legend Badge, in Pokémon White. Two years later, in Pokémon Black 2 and White 2, she is the Champion.
In the Anime:
Iris is a girl from the Unova region who is a former traveling companion of Ash Ketchum. She is a Pokémon Trainer but does not hold any specific title e.g. Gym Leader, Elite 4 Member, Champion etc. However she did win the Club Battle tournament that was held in Nimbasa Town. Also after she returned home to the Village of Dragons, she received the opportunity to re-battle Drayden this time in a Gym battle. Even though she lost she displayed much improvement and promised to get stronger, as a result Drayden told the village elder to consider Iris as the Opelucid City Gym Leader.
Iris has a particularly strong understanding of Dragon types and tends to be very excitable around them in particular, not showing fear even against a rampaging Druddigon. Because of this strong passion, she aims to become a Dragon Master like so many others from her hometown.