What do Sith do? Use lightsabers and the Force. What do Inquisitors do? Yeah, the exact same thing.If you care enough, then yeah.
And if they were Sith, sure, but they're not and have never been described as Sith. It's only contradictory if you can't be bothered doing a 30 second search on Google. The end. Period.
Sith actually meant a species from Legends canon. So really what is a Sith? Google can tell me different things so which one is it? A species or dark side force users? Or is it dark side "Lords" or "Darth" or "Master"? But Master is used for Jedi so what is it now then?
Live action is pretty clear cut. They will continue down the contradictory path for money's sake. Period.