The novel dispels the mystery pretty bluntly: they're not. Ninny is seen interacting with Idgie in several flashback sequences, and Ninny is established to have married Idgie's older brother Cleo, which is how she got the Threadgoode name. While it's possible that Older Ninny is an Unreliable Narrator who is repeating these sections to Evelyn as if she and Idgie are different people, there's no indication that the flashbacks are being related to anyone other than the reader (and many of them are scenes that Ninny could not have witnessed, such as the modern-day scene with adult Stump and his daughter). Ninny knows about Frank Bennett because Sipsey made a Deathbed Confession to Mrs. Otis (Ninny's roommate at the retirement home), and Mrs. Otis told Ninny. Moreover, the book's final chapter reveals that Idgie is still very much alive after Ninny herself has died. The sequel, which covers up to 2019, discusses the deaths of both characters, and makes it even clearer that they are not the same person.
The film evidence for Ninny and Idgie not being the same person is more tenuous: during the wedding scene at the Threadgoode house, Buddy comes through the kitchen bearing Idgie on his back. They both say "Hi, Ninny" to a teenage girl helping with the preparations. This is the only confirmation we have that Ninny and Idgie are definitely two separate people...but since we know for a fact that Old Ninny is telling this part of the story, she really could be an Unreliable Narrator.
The best evidence is the film's final scene, where Ninny shows Evelyn Ruth's grave. The two of them walk a short distance with their backs to the grave. When they return, they find a jar of honey and a note from Idgie on Ruth's previously bare grave. Since Evelyn does not take her eyes off Ninny during their walk, there is no opportunity for Ninny to have left the jar.