There is no difference. Just label anything you want to censor as propaganda.

That is a unsubstantive statement in my view. Who is labeling here, why and what context?

In any context. If someone thinks or knows something is propaganda they should exercise their free speech to point that out.

Not even propaganda should be censored.

Then again propaganda often implies it’s coming from a government. In that case the people and their representatives should have the power to prevent or retract statements if needed.

Maybe not, it is certainly debatable. But propaganda implies (to me at least) it has gone beyond debate. It also implies a tool to influence others. Aka a form of weaponized information. I do think there is a gradient where one could say “this goes beyond free speech” , for instance as in your example.

This is what someone with a high stake in propaganda would say. Fact is, there is a difference.