Last time I used GPT-4.5 to analyze blood results it gave different output if I uploaded it as 2 instead of 3 separated CSV files. It was both amazing experience: clear and easy to understand statements, and list of most common causes. And terrifying: "What about X?", "You ar absolutely right, there where X results included, disregard everything I wrote above, here is the new analysis".
So for me non-deterministic means unpredictable. Yes, there was nothing random or non-deterministic in that case, I could repeat both scenarios multiple times and get same results again. But the result is affected by something I didn't expect to matter. That damages the trust in tool, no matter how we call it.
LLMs seem best at creative brainstorming, coming up with ideas to check that you hadn't thought of. Their weakness becomes a non-issue because ideas are just things for you to check the viability of, because they could be completely unworkable.
So for me non-deterministic means unpredictable. Yes, there was nothing random or non-deterministic in that case, I could repeat both scenarios multiple times and get same results again. But the result is affected by something I didn't expect to matter. That damages the trust in tool, no matter how we call it.