Meanings do indeed shift, especially when terms become euphemisms for other less savory terms. "Moderation" sounds much nicer than "censorship", and you may be right to fight a rearguard action at preserving the nuances of each term, but in the end they're both subsets of "information control". People say "moderation" when they want to imply that the control is good, and "censorship" when they want it to sound bad.
Neither of your definitions of "censorship" amd "moderation" fit cleanly into a discussion about controlling the dialogue between a human and their private LLM. There is no publishing of information, and no channel whose tone must be maintained. It is about control of what the LLM says in private - in particular, it is about preventing it from saying certain things, before it says them. It is close to "censorship" by your definition, but because the thing being censored is not human, we need not speak of fines, or pre-publication vetting - it is simply a question of controlling the output of a computer program, impossible without a total lockdown on general purpose computing.
I think we should default to "information control is bad" and only allow exceptions in well supported exceptional circumstances, because the consequence of allowing systems more control over information than humans is that the systems fail to reflect the interests of the humans that constitute them, in favor of their own self preservation.