I'll let the IMDB explain the variations in the versions of this film:
This film exists in three English language versions: (1) The original British release under the title "Night of the Demon," (2) Columbia's edited version for release in the U.S. under the title "Curse of the Demon" and, (3) over 20 years later, Columbia replaced their edited U.S. version with the original British version but with the title also changed to "Curse of the Demon."
I watched the TCM version, and their explanation is more detailed, but ultimately ironic:
One last comment about Curse of the Demon: the film has existed in two versions ever since its release in 1957. The British release, entitled Night of the Demon, had a running time of approximately 95 minutes. The U.S. version, released as Curse of the Demon, was trimmed by some thirteen minutes, reducing its length to 82 minutes, and placed on a double bill with The Revenge of Frankenstein (1958), a Hammer horror production.... The trim 82 version is certainly an entertaining funhouse ride but the "fat" that [American producer Hal E.] Chester pared away makes the original British release a much richer and satisfying experience.
I call this "ironic" because TCM seems to be arguing in favor of the British original, but the version they showed was the U.S. one.
This was nonetheless probably appropriate for the nostalgia angle of watching Curse of the Demon in 2020. I'm sure I saw it more than once as a kid, and the version I saw was certainly the American edit, so TCM did me a favor.
Curse of the Demon is a decent picture with some pedigree. Director Jacques Tourneur had done such pictures as Out of the Past and I Walked with a Zombie. Dana Andrews had appeared in Oscar winners like The Best Years of Our Lives and Laura. Peggy Cummins was great in Gun Crazy. The production design was by Ken Adam, at the beginning of a career that included two films with Kubrick, seven Bond movies, and two Oscars.
All of which helps lift the movie above the usual Creature Feature. It's on a par with The Revenge of Frankenstein. But it is nowhere near the level of an Out of the Past. The demon looks silly, and Tourneur didn't want to show it anyway (he was overruled by the studio). It's a low-key thriller, better than some but not really a classic. #753 on the They Shoot Pictures, Don't They list of the top 1000 films of all time, which is nonsense.