Fancy autocomplete. Useful, yes. Powerful, definitely. But it's just another tool, limited in applications the same way a hammer is - this is the part that many humans seem to struggle accepting.
Philosophy of language, and Wittgenstein in particular, has more specific words for the output insofar as they mean anything to humans: "senseless" or "nonsense".
You've just re-presented one difference between sense and nonsense in philosophy of language. We might call that first phrase wrong or an error or inaccurate if that was the case. We don't need to use a word like "hallucinate" for your second phrase --- we can just call it nonsense.
"Hallucinate" is far more inaccurate and confusing. It paints a false picture that melds 2 distinct things, as you've described, which need not happen at the same time: errors and nonsense.
When a human hallucinates, that is due to the brain operating out of spec. When an LLM "hallucinates", it's performing exactly as intended, it just has delivered a nonsensical result which is the consequence of the tech behind the LLM.
https://link.springer.com/article/10.1007/s10676-024-09775-5
Isn't Frankfurt's concept of bullshit made up of 2 parts: 1) a distinction between lying and telling the truth, AND 2) the absence of caring about either when speaking when normally it's assumed present?
Part 1 seems to apply, but part 2 wouldn't. It doesn't make sense to talk about GPT "caring" about its output beyond anthropomorphism. No one talks about their computer caring about having correct or accurate output and neither is it assumed. People would think your imagining a demon in the box. Really, it's even odd to say "GPT lied" outside of very specific circumstances.
Maybe we just need to coin a new word for it - "LLM-ing" perhaps ?!