Fixed input-to-output mapping is determinism. Prompt instability is not determinism by any definition of this word. Too many people confuse the two for some reason. Also, determinism is a pretty niche thing that is only necessary for reproducibility, and prompt instability/unpredictability is irrelevant for practical usage, for the same reason as in humans - if the model or human misunderstands the input, you keep correcting the result until it's right by your criteria. You never need to reroll the result, so you never see the stochastic side of the LLMs.
It really depends on your perspective.
In the real world, everything runs on physics, so short of invoking quantum indeterminacy, everything is deterministic - especially software, including things like /dev/random and programs with nasty race conditions. That makes the term useless.
The way we use "determinism" in practice depends contextually on how abstracted our view of the system is, how precise our description of our "inputs" can be, and whether a chunked model can predict the output. Many systems, while technically a fixed input/output mapping, exhibit an extreme and chaotic sensitivity to initial conditions. If the relevant features of those initial conditions are also difficult to measure, or cannot be described at our preferred level of abstraction, then actually predicting ("determining") the output is rendered impractical and we call it "non-deterministic". Coin tosses, race conditions, /dev/random - all fit this description.
And arguably so do LLMs. At the "token" level of abstraction, LLMs are indeed deterministic - given context C, you will always get token T. But at the "semantic" level they are chaotic, unstable - a single token changed in the input, perhaps even as minor as an extra space after a period, can entirely change the course of the output. You understand this, of course. You call it "prompt instability" and compare it to human performance. But no one would call humans deterministic either!
That is what people mean when they say LLMs are not deterministic. They are not misusing the word. It just depends on your perspective.
This is all currently irrelevant, making it work well is a much bigger problem. As soon as there's paying demand for reproducibility, solutions will appear. This is a matter of business need, not a technical issue.
However, if you evaluate carefully the LLM core function, i.e. in a fixed order, you will obtain perfectly deterministic results (except on some consumer GPUs, where, due to memory overclocking, memory errors are frequent, which causes slightly erroneous results with non-deterministic errors).
So if you want deterministic LLM results, you must audit the programs that you are using and eliminate the causes of non-determinism, and you must use good hardware.
This may require some work, but it can be done, similarly to the work that must be done if you want to deterministically build a software package, instead of obtaining different executable files at each recompilation from the same sources.
This is a good overview of why LLMs are nondeterministic in practice: https://thinkingmachines.ai/blog/defeating-nondeterminism-in...
The deterministic has a lot of 'terms and conditions' apply depending on how it's executing on the underlying hardware.