I don't see how using propaganda would imply that the same information are being sewn multiple places.
Propaganda is merely the focused government effort to understand and engage key audiences to create, strengthen, or preserve conditions favorable for the advancement of government interests, policies, and objectives through the use of coordinated programs, plans, themes, messages, and products.
Different audiences are going to require different messaging.
The US's propaganda is quite different than China's propaganda when it comes to the exact physical end product, although the countries are starting to share more and more common tactical forms and procedures.
Of course what the US wants US civilians to think is different than was the US wants China to think is different from what US wants Chinese civilians to think is different from what China wants USG to think is different from what China was US civilians to think.
Propaganda is not a blunt instrument. It has to be and is targeted to specific audiences.