I think it depends on the specifics and I can struggle to find the right terminology sometimes. I find that working on when to use which term can be helpful for reminding oneself of exactly the problems with the claims they've made, and what can be proven.
When they've said something which is provably false, can just say it's 'false'. More cautiously: inaccurate? not true? For claims that are merely misleading, 'misleading'. Sometimes they say things that are not clearly false, but are unjustified, and pointing that out can be helpful. Over the last few years I've pick up a lot of different ways of politely describing quackery!
I think that matter of factly stating 'that claim is not true' and explaining why is usually more powerful than saying something is bullshit or nonsense.
I think it is much easier, and potentially more subtly powerful, to state what is objectively discernible fact. Once you start making accusations of someone's reasons for doing or saying something, then that is subjective and much harder to prove, and much much easier for the person to reject as being a personal attack on them. So if someone publicly states that they caught a fish weighing a ton, you can either state that they said they caught a 1-ton fish, or state that they lied about catching a 1-ton fish. The former is indisputable if it is on record, but whether it was truly a lie needs deeper and more tricky investigations, possibly with legal interventions.
@dave30th is very good at getting this right. Often stating untruths that are clearly evident to all, allowing readers to make their own inevitable inferences of people's motivations for stating their untruths.
There is another powerful bit of psychology here, that I myself have realised over the years. Effective communication is the overall goal, which involves not just transmitting of information, but effective receiving of that information,
along with effective processing of it. That latter bit - processing the information - is a crucial final step in the chain of communication. And a very effective way of achieving that is to get the reader/listener to actively engage in the information-exchange process, give them something to do. This means not handing them every single morsel of information to them on a plate. Instead, motivate them to think about what is being said, and then mull it over themselves, think about it and come to some of their own conclusions. Stating the clear truthful facts, without actually stating people's motives, forces people to think about people's motives, and realise there have been lies told.
This of course is what the 'other side' do, but with far less integrity. They state
partial facts, that by omission amount to their readers inevitably inferring falsehoods. Their readers then, based on strongly implied untruths, infer that people like us are liars, vexatious agitators, etc. But we have truth on our side, which the BPS crew are rightly scared of, and so we need to just use the same basic strategy, but based on the whole truth - that is very powerful, and something the other side have no real defence against. e.g. "Have you actually read the paper?"
