Science-Fiction; Political Thriller; Parable
Pro-tip: if it's Star Trek, it's science fiction. Unlike Star Wars, which takes a fantastical approach to its interstellar setting, Star Trek tries to remain grounded in real science.
Of course, we do meet God back in Star Trek V, so take that with a grain of salt.
Either way, Star Trek's foundational scientific concepts are usually somewhat plausible, albeit a bit far-fetched, making Star Trek VI a classic example of hard science fiction.
The Undiscovered Country is unique among the Trek film series due to its almost exclusive focus on political issues. Seriously, if you removed the sci-fi trappings and set the story on planet Earth, it would be some cool espionage thriller starring Ben Affleck or Kiefer Sutherland. We'd watch that.
There's an obvious reason for all of this: the film is a pretty direct parallel to the peace process going on between the Soviet Union and United States. Many Star Trek stories can be described as parables—stories that indirectly convey a moral lesson or analogize a real situation—but The Undiscovered Country is especially literal in that regard.