What is the difference between a denouement and a resolution? Are they synonymous?
According to my dictionary 'The Collins school dictionary'
'The denouement of a story is the explanation at the end of it of something that has previously been unclear or kept secret.'
While Resolution has several definitions, the relevant one I feel being: 'The resolution of a problem is the solving of it.'
It doesn't specifically mention in a story but it's the closest my dictionary has.
From this I would surmise that the difference is that a denouement has to have some secret or mystery about it while a resolution doesn't.
E.g. A story about an orphan boy of unknown birth having and fulfilling a destiny to overthrow a tyrant king, only for it to turn out that the boy is in fact the long lost prince and the rightful heir would have a denouement as the boy heritage was unclear.
While a story about a prince in exile raising a popular uprising to oust the usurper to the throne would have a resolution as there is no secret about any of the characters.
Start with a dictionary instead of google.
the end of a story, in which everything is explained, or the end result of a situation
It is the end of the story.
the act of solving or ending a problem or difficulty
The denouement (end) of a story may contain a resolution for the problems encountered in the story - or not. Some stories intentionally end without a resolution. They leave the problems unresolved in attempt to get the read to consider and think about a solution.
From a strictly definitional standpoint, the other answers here do an outstanding job, but some good popular examples would be revealing. I feel this is best illustrated by a series of examples. WARNING this may contain spoilers.
In the movie Lucky Number Slevin (a slightly obscure favorite of mine), the resolution is the main character, Slevin Kelevra, defeating the bad guy. The denouement is
Slevin is a false name, and the main character has been raised by the assassin that was supposed to kill him along with the rest of his family when he was a child. All revealed to the bad guy just before Slevin kills him in revenge.
In the movie Signs, the resolution is the family surviving the night of terror and being safe. The denouement is
discovering that all the seemingly random misfortunes that have happened to the family for years are all a divine conspiracy to assure the family has the tools to defeat the aliens attacking them.
In The 6th Sense, the resolution is the little boy revealing his psychic abilities to his Mom and convincing her of their validity. The denouement is
That the therapist the boy has been working with is actually a ghost, and while the therapist has been helping the boy with the boy's issues, the boy has been helping the therapist move on by the therapist redeeming himself.
The last one is particularly good, since the resolution also involves revealing secrets.
Defnitions of the term 'dénouement' differ, as shown in the listings on Wordnik - with the term being variously defined as both 'final resolution' and as 'outcome':
from The American Heritage® Dictionary of the English Language, 5th Edition.
noun The final resolution or clarification of a dramatic or narrative plot.
noun The events following the climax of a drama or novel in which such a resolution or clarification takes place.
noun The outcome of a sequence of events; the end result.
Etymology gives a better clue as to the distinction between the terms 'dénouement' and 'resolution'.
According to the Online Etymology Dictionary, dénouement has the following origins:
"the solution of a mystery, the winding up of a plot, the outcome of a course of conduct," 1752, from French dénouement "an untying" (of plot), from dénouer "untie" (Old French desnouer) from des- "un-, out" (see dis-) + nouer "to tie, knot," from Latin nodus "a knot," from PIE root *ned- "to bind, tie."
It is related to the Greek peripeteia.
It lists 'resolution' as being derived as follows:
late 14c., resolucioun, "a breaking or reducing into parts; process of breaking up, dissolution," from Old French resolution (14c.) and directly from Latin resolutionem (nominative resolutio) "process of reducing things into simpler forms," noun of action from past participle stem of resolvere "to loosen" (see resolve (v.)).
From the notion of "process of resolving or reducing a non-material thing into simpler forms" (late 14c.) as a method of problem-solving comes the sense of "a solving" (as of mathematical problems), recorded by 1540s, as is that of "power of holding firmly, character of acting with a fixed purpose" (compare resolute (adj.)). The meaning "steadfastness of purpose" is by 1580s. The meaning "effect of an optical instrument in rendering component parts of objects distinguishable" is by 1860. In Middle English it also could mean "a paraphrase" (as a breaking up and rearranging of a text or translation).
In mid-15c. it also meant "frame of mind," often implying a pious or moral determination. By 1580s as "a statement upon some matter;" hence "formal decision or expression of a meeting or assembly," c. 1600. New Year's resolution in reference to a specific intention to better oneself is from at least the 1780s, and through 19c. they generally were of a pious nature.
A resolution is something reached through a process of weighing up and sifting options, then coming to a decision. This process can often be a launching pad that leads to a new set of actions. Crabb confirms this reading by defining resolution (in the sense of the reaching of a decision) as a minor form of courage - a decision to proceed along a course of action.
It would therefore be useful to think of how endings or 'landing points' function in stories and look at the difference in function to clarify the difference in terms here.
Often a subplot can end in an outcome which provides a new problem. In the story of The Three Little Pigs, the outcome of the wolf's attempt to eat the first little pig is either that the pig escapes him, or that the pig is eaten ... either way, he's left hungry. As a result, he resolves to set out once again in search of food, which isn't good news for the other two pigs.
Personally, I find it useful to think of these 'landing points' as 'outcomes', which can be positive or negative - and of the final resolution (which can also be happily positive or tragically negative) as being the point at which all of the loose ends and plot twists are resolved and the story brought to a close.
In the case of nested stories, such as The Arabian Nights, each nested story will have its own resolution within the larger frame story. In the larger frame story, the resolution is delayed, which is what allows the form to expand.