The Enterprise stops at planet M-113 to resupply the scientist working there, Dr. Robert Crater, and to permit Dr. McCoy to perform a mandatory annual medical exam. Dr. Crater's wife, Nancy, is an acquaintance (and former romantic interest) of Dr. McCoy. When McCoy sees Nancy, she looks to him exactly as she looked when last he saw her, twelve years earlier. This is only the most innocuous mystery on M-113, though, for soon a crewman is found dead, his body drained of salt.
It turns out that a shape-shifting creature native to the planet killed the crewman, and years prior Nancy, out of a desperate need for salt. As it is the last of its species, Dr. Crater could not bring himself to kill it. In the end, though, McCoy is forced to kill the creature to save Kirk.
Notes
The substance of the story is in two main parts: first, the mystery of just what's happening, which is not too hidden from the audience; second, moral questions as to whether the lie that the Professor was living is worthwhile, and what is the right action to take with regards to the creature–they compare it to the buffalo, driven to near extinction.
I'm reminded of the Coeurl from van Vogt's Black Destroyer.
This is an early episode, so they don't have the characters nailed down, yet. When Kirk says he'll put his phaser on stun, Spock asks him "Why risk your life for his?" and Kirk must explain to him that, after all, Crater is not trying to kill them, just scare them off. By the time of "The Galileo Seven", Spock had changed his tune!
There were smaller differences, too. One that stood out to me was the log entries: they later settled on "Captain's Log, supplemental" for additional narration but in this episode, rather than 'supplemental', Kirk used 'additional entry' or 'continuing'. A small thing, to be sure, but a little jarring.