Philosophically, and scientifically, the distinction is vast (even with such perfect data). A scientist should not study an LLM to understand how imagination operates, since it has no such faculty. A philosopher should not modify the notion of 'mental simulation' to include appearing-as-if-simulating-in-text. A user of the system likewise should not spiral into "AI psychosis" thinking that because a system generates text as-if it cares about them, it does so.
The capacity to care, to imagine, to prefer, to hierarchically plan and coordinate, to refine one's own capacities in these very actions -- and so on, aren't trivial to the scientist or philosophy.
My goal isnt to guide, help or review the engineering goal of the immitation of such things in text. It is to help users of these systems better understand this imitation, and to promote science over engineering. To remind everyone that a science of the capacities of intelligence includes nothing on how to model text.
EDIT: One example of a place where LLMs 'fall over' today is exactly what is mislabelled as 'alignment'. The issue is that the reasoning traces arent actually grounding the answers. So LLMs appear to 'cheat'. But there is no cheating. LLMs have been rewarded for generating apparently correct reasoning, and apprently correct answers. They have not been given any understanding to derive answers from reasons. And so reasoning says what is pleasant to the trainer, and the completion says what is pleasant to the user. This is called 'cheating'. But it is no such thing.
On alignment, too, there doesn't seem to be a difference. For a decade I have expected models of intelligence to fall over on alignment. That these purported models of language do the same is hardly evidence that they are not intelligent.
If you only mean there is an undecidable philosophical difference, fair enough. I'm not especially interested in that question.
To study an imitation is to study the causal processes of imitation. to study reality is to study the real causal processes.
Now if you want to know what the scientific difference is I can come back later and comment. I'm busy now. The development of intelligence in animals and how their specific capacities work basically grounds the answer. Eg., to have the capacity to imagine is to be able to modify one's sensory-motor relationship to the environment in the future, and so on
LLMs are immitation machines: they take impressions of prior text. Today, these include reasoning traces and they include reinforcement so the user-facing completions are correlated with these reasoning traces. The computation here, of "taking an impression" of a data distribution is similar to some impression-taking processes in animals (eg., there's no doubt a similar mechanism in the sensory-motor system acquiring initial impressions of external objects) -- but the computation says nothing about any process of intelligence.
I dont have the time atm to write the needed amount on this to make it clear. But the whole history of life from emergence of valence, bilateral symeterry, to model-free reinforcement and model-based reinforcement, sensory-motor coordination and the imagination -- and so on --- all these give a great amount of detail as to what the capacities of intelligence are which has generated this text for LLMs to copy. And they are nothing like this computation of immitation