“It’s so metaphorical!” Kim Ki-woo exclaims early in “Parasite,” Bong Joon Ho’s new film. Ki-woo is the college-aged son of one of the two families — the impoverished Kims and the wealthy Parks — whose fates entwine with horrible and hilarious results. He uses the phrase a few times, most notably with reference to the large, decorative “landscape rock” that is a gift from a better-off friend. In the interpretation of “Parasite” that emphasizes the movie’s fairy-tale aspects, the stone brings good fortune to Ki-woo, his sister and their parents, even as, like so many magical objects, it also curses them. (Spoilers follow, for “Parasite” and other Bong movies.)

Before long, Ki-woo stops talking about metaphors. Maybe because things start getting real. He takes a job tutoring the Parks’ teenage daughter, Da-hye, and pretty soon his whole family is employed, under dubious premises and fake identities, in the Park household. His sister, pretending to be a highly trained art therapist, starts working with Da-hye’s younger brother, Da-song. The Kim patriarch, Ki-taek, replaces the chauffeur who drives Mr. Park to and from his fancy tech job. Kim Chung-sook, the mother of the clan (a former Olympic-level hammer-thrower), takes over as housekeeper.

Or maybe — and it might amount to the same thing — the Kims’ reality has turned into an unsettling allegory of modern life, and Ki-woo doesn’t see metaphors in the way that a fish doesn’t notice water. What started out as a clever scam has turned into a fable.