I think OP is saying that hallucination or not is just semantics. There is nothing qualitatively different about hallucinated vs non-hallucinated output.
That's true in the same sense as "There is nothing qualitatively different about erroneous vs non-erroneous output" for a dog vs. cat image classifier.
That's true in the same sense as "There is nothing qualitatively different about erroneous vs non-erroneous output" for a dog vs. cat image classifier.