That’s because they’re the same thing in different languages. I learned the same propaganda as you; the distinction taught to us was basically made up.
"Rule of the People" and "Concern of the People" sound SIMILAR, sure!
Just because a mechanic is concerned for your car, does not mean he owns it... I think it's lazy of you to call this dichotomy "propoganda" without offering any definitions or etymology.
One is Roman. One is Greek. They describe the same concept, but it’s a concept that has been implemented differently both in their time and in ours: self-government. The forms and institutions are distinguishable as “Roman-style” or “Athenian-style”, but the same is true in 2022 of “American-style” and “French-style” republics.