The RE franchise has always had a weird interrelationship between the games and the movies; though both follow roughly the same plot of a viral outbreak, there are many, vital discrepancies between the two; though many game characters reoccur in the movies, the movies are never explicitly about the game characters; though the games touch on many emotional subjects surrounding a viral outbreak, the movies are almost exclusively about Milla Jovovic's kung fu.
The plot of the games revolves around four main characters (Chris, Jill, Claire and Leon) and deals with them coming to terms with a mass outbreak of various viruses (the T-Virus, and las Plagas, to name the main culprits), which have been engineered by the company they used to work for: Umbrella. The games follow the characters in their various attempts to thwart Umbrella, close down their labs, and generally save the world.
The movies were an accidental success; director Paul W S Anderson only intended on shooting one movie, which was supposed to be a tie in to the games, a la Stargate (different stories existing in the same universe, never interacting). He wrote a script full of Alice in Wonderland references (hence the main character's nickname), and turned the movie into an exhibition of his wife's ninja skilzz. The movie did not go down well with game fans, but the rest of the world loved it, and so the RE franchise was born, and Anderson bailed out of the director's seat in order to concentrate on the script, and so the story continues. The next movies loosely followed the game plot, with a few familiar characters showing up, but after 5 movies the plot is still centered around 'Alice', a stand in for the gamer.
The fandom is ultimately split down the middle: those who love the games and get all antsy about the existence and worldwide popularity of the movies, and those who love RE regardless.
In summary: Resident Evil is not a zombie story.
( cut for spoilery speculation on movies 5&6, and discussion of gaming meta )