A Tale of Two Sisters is a 2003 South Korean horror film. Wikipedia says, "It is both the highest-grossing Korean horror film and the first to be screened in American theatres." The story is based on a Korean folk tale that has had numerous film adaptations. This is the only version I've seen, but here the story is told primarily in flashback. It begins with one of the sisters sitting with a doctor who asks her to tell him about "that day". Identities are interesting in this one. It would make a fun psychological study.
Moria says the director "attains a more than reasonable degree of haunted effect" but that the twist ending is a problem. Slant Magazine says it's "an exercise in internal horror". Rotten Tomatoes gives it a score of 86%.