>Fixed input-to-output mapping is determinism. Prompt instability is not determinism by any definition of this word
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.