It was a mix of both fantasy and science fiction. It was largely fantasy, and many of its SF episodes had fantasy elements in them (e.g. "Death Ship" or "And When the Sky Was Opened"), but there were plenty of straight-up SF stories without anything supernatural or surreal about them -- "The Lonely," "Time Enough at Last," "I Shot an Arrow Into the Air," "The Monsters Are Due on Maple Street," "Eye of the Beholder," "The Invaders," "Will the Real Martian Please Stand Up?," "The Obsolete Man," etc. I'd even call something like "Back There" or "A Hundred Yards Over the Rim" science fiction; the mechanism of time travel in those cases is never explained, but it isn't overtly supernatural either.
For that matter, there were a couple of TZ episodes with no SF/F elements at all, "The Silence" and "The Jeopardy Room." Those were thrillers more in the vein of Alfred Hitchcock Presents, with twist endings but no unrealistic elements. And the pilot, "Where Is Everybody?", barely counts as SF, because there was a rational explanation for the weirdness (a result of the network being cautious about the fantasy aspects).
