The Inquisitors aren't Sith Lords in Star Wars despite being dark side Force users and Darth Vader's minions — and the reason goes back to the Sith Order's convoluted rules. Star Wars is a complex franchise with hundreds if not thousands of contradictory storylines and retcons, but those minor issues pale in comparison to the multitude of rules that members of various groups and orders have to contend with — the Sith being one of them.
Much like the Jedi, the Sith follow an ancient religion that revolves around the Force, though for them it's all about power, passion, and succumbing to the dark side. But just because someone follows the dark side of the Force and wields a red-bladed lightsaber, that doesn't mean they're Sith. Anyone can wield a lightsaber in Star Wars; it doesn't require being Force-sensitive, but being a Jedi mandates adherence to the Jedi Code. In a similar fashion, being a Sith means following the Sith Code as well as the Rule of Two.
Related: Why Obi-Wan's Grand Inquisitor Looks & Sounds So Weird
Following the Jedi Purge in Star Wars canon, Emperor Palpatine fulfilled his plan to establish the Inquisitorius, an organization of dark side Force users dedicated to hunting down the Jedi who survived Order 66. Darth Vader led the group, which was commanded by the Grand Inquisitor, a former Jedi Temple Guard. Still, the Grand Inquisitor — nor any other Inquisitor — wasn't Vader's apprentice, and therefore, wasn't a Sith. The Inquisitors are agents of the Sith, but not Sith themselves because they exist outside of the Rule of Two.
It's possible that the Inquisitors could've become Sith if they existed in the Old Republic when the Sith Order numbered in the thousands. But things were different in the Age of
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