Wouldn't 'illusion' be the more precise term here ? When one thinks he recognizes something, whereas 'hallucination' is more of unreal appearing out of the blue ?

You might be thinking of deepdream... https://en.wikipedia.org/wiki/DeepDream

"Hallucinations" have only really been a term of art with regards to LLMs. my PhD in the security of machine learning started in 2019 and no-one ever used that term in any papers. the first i saw it was on HN when ChatGPT became a released product.

Same with "jailbreaking". With reference to machine learning models, this mostly came about when people started fiddling with LLMs that had so-called guardrails implemented. "jailbreaking" is just another name for an adversarial example (test-time integrity evasion attack), with a slightly modified attacker goal.