Somewhat different circumstances. It was set after TOS and had feature film budget for makeup and effects and until the reboot movies retained the same appearance in multiple films and TV series.
Hardly the same. There were numerous differences between the Klingon designs of Fred Phillips on TMP (a single central spinal ridge on an otherwise smooth bald head, the same for every individual), the Burman Studios on TSFS (thick bony head plates with individualized bump patterns, minimal ridging on females), Michael Westmore on TNG through ENT (Burman-style head plates with TMP-style nasal ridges and no gender differentiation), and Richard Snell from TVH-TUC (thinner, rounder head plates with more intricate individualized ridging, again minimal on females).
https://www.herocollector.com/en-us/Article/star-trek-the-many-faces-of-the-klingon
Prosthetic makeup is an art form. Different artists bring their own distinct style and design sensibilities to their work. So of course every new Trek makeup designer has taken the opportunity to reinvent the Klingons in some way, to devise their own personalized variation on the basic themes laid down in TMP and TSFS.
And if it is perfectly justifiable to radically change how Klingons are depicted after 3 or 4 decades, why not Vulcans?
Actually a good question. Different Trek makeup (or digital) designers have come up with their own distinct variants for many Trek species -- not just Klingons, but Andorians, Tellarites, Romulans, Gorn, Saurians, Barzans, etc. And yet the Vulcan design has remained pretty much constant. I'd conjecture it's because Spock is such an iconic, central character that nobody wants to tamper with his look too much. And so other Vulcans maintain a consistent look by association.
Then again, maybe it's because Vulcans are so humanoid. There are other instances where humanoid aliens are kept fairly consistent in their look from designer to designer. Michael Westmore's Tiburon makeup from DS9 closely replicates Dr. Sevrin's ear design and just adds a vertical ridge of small forehead horns. Westmore's Orion women in ENT looked pretty much exactly like the TOS version, as do the
Discovery Orions; the only difference was that Westmore gave Orion males elaborate head piercings.