There can be many reasons due to which anything can seem artificial.Consider a case of movie.When can we say that movie is contrived and, when stilted?
When talking about a movie, I think you would be more likely to say it is stilted if you are specifically referring to the writing or acting being poorly executed.
I had a hard time enjoying that movie because of the stilted writing.
The main character's acting was so stilted I wished she had been relegated to the role of eye candy.
Stilted gives the impression that the artist has failed in the execution of their art and the result is that it seems unnatural and not pleasing. It pretty much means the writer or actor did a poor job.
The word contrived gives the sense that something is overcomplicated in an unnatural way in order to achieve an artificial goal. For example, the writer wanted to arrange a romance between two characters, so they ended up stranded on an island in a way that doesn't make sense in the overall plot.
The special effects in Pacific Rim were fun, but the plot's introduction of robots was so contrived I could hardly sit through it.
The plot of a movie is often the thing that is contrived.
Well, they are both synonyms of each other; however, they aren't always used interchangeably. I normally hear people say something is "stilted" when talking about language:
"John's speech last night was so stilted. He casually threw out words like "shall" and subjunctive clauses as if he had been quoting from Shakespeare."
I usually hear "contrived" when talking about a plan or a plot in a novel:
"It was clearly a plan the was contrived poorly, which is why it fell apart so quickly."
"The ending of the novel is clearly contrived as it has almost no chance of happening in real life."
To add on to the other good answers:
In the context of a movie, "stilted" relates to the performance, while "contrived" relates to the story.
The way he said that long speech was stilted and unnatural.
The plot twist where they suddenly found the missing MacGuffin was too contrived to be plausible.
Again, when talking about a performance, both of these violate the audience's suspension of disbelief:
suspension of disbelief: a willingness to suspend one's critical faculties and believe something surreal; sacrifice of realism and logic for the sake of enjoyment
With a stilted performance, the audience recognizes that what they are watching is an actor playing a part, and not the actual character embroiled in some dramatic moment.
Meanwhile a contrived story is one in which what happens is so artificial, or unexpected, as to force the audience to recognize they are watching a work of fiction, and not a witness to a real-world drama. A classic example of this is the Deus ex Machina:
Deus Ex Machina: when "some new event, character, ability, or object solves a seemingly unsolvable problem in a sudden, unexpected way."
There are many variations, such as when the sidekick (who everyone thought dead) shows up to kill the bad guy just before he's about to kill the hero. While this can be well done, often the sidekick's rescue is through some contrived plot device: a previously unseen rope, previously undisclosed armor, etc.
'Contrived' is used in the context when the movie becomes too formal, losing its natural script and thus becomes predictable to the extent that a viewer can derive the next moment or dialogue easily.
Whereas if you are referring to it as 'stilted', that would mean the script or the dialogue of the movie is too formal that it can be referred as an artificially unnatural presentation of its overall plot.
Check Oxford dictionary's definitions as well: