> Learning" is an established word for this

Only by people attempting to muddy the waters.

> happy to stick with "training" if that helps your comprehension.

And supercilious dickheads (though that is often redundant).

> No copy is created until output is generated that contains a copy.

The copy exists, albeit not in human-discernable form, inside the LLM, else it could not be generated on demand.

Despite you claiming that "It works exactly the same for a LLM," no, it doesn't.