If you generalize enough, all "revelations" are ultimately "surprises", the characters (and often readers) are led to believe one thing, and by some means or another discover this is not true. And perhaps the truth.
This is quite often in the finale, to provide a twist at the end. It may also be early, like in the first Act. In most stories, there is an "inciting incident" at about the 10%-15% mark in the story, roughly the middle of the first act, which grows into a problem for protagonist that makes the protagonist ultimately leave their "normal world" at the end of the First Act (about 25% of the story).
That inciting incident can be a revelation. It doesn't have to be, it can be an accident, some job incident. A death in the family. But it might be a disease diagnosis -- a revelation. It might be discovering their spouse is cheating on them -- A revelation. It might be discovering your boss is a criminal embezzling from the company -- A revelation.
Along the way in the story, the 3 act structure has about 15 turning points, and any one of them may be cast as a revelation. This is often the case in adventure stories or mystery stories -- The protagonist puts some clues together (a revelation) and collects another piece of the puzzle, or knows where they have to go next. Or discovers a rival, or another player, or figures out a previous mystery about who they are up against.
I don't know how to classify revelations. Perhaps by where they occur in the story. Perhaps by how long they must be teased. For example, clearly the finale revelations have to be teased for nearly the entire story, while some of the adventure or mystery revelations may be only teased for a short time, a chapter, or even less.
For example, In the Dan Brown movies the protagonist follows a trail of clues sequentially, the audience (and protagonist) does not get the next clue until they solve the current clue.
But in other novels or movies, the audience is shown something that the protagonist does NOT know, and that is either a midpoint or finale revelation.
The old TV series Columbo did this religiously; they showed us the murder and murderer, and then the entire show is about how Columbo (A Sherlockian Detective), oblivious to this knowledge, figures out the Whodunnit by the clues.
So to me the timing is not about when the audience knows, it is about when the protagonist knows. In both of your examples, when Bruce Willis knows (As Dr. Michael Crowe in The Sixth Sense, and as David Dunn in Unbreakable).
