It's different in the same way that making a copy of a book by hand, where it might take weeks or months to make a single copy, is different than making a copy with a printing press in a few minutes. It was the technological development of the latter process which lead to the concept of copyright being created in the first place.
There is a fundamental difference between a human being taking years to acquire artistic skill, then using that artistic skill to create individual works inspired by other artists, vs. using a generative AI system to "learn" a particular artist's style in a minutes or hours, then create infinite iterations of that style nearly instantly.
There's a tendency for people in tech to search out broad, overarching, universal principles that can be applied to all behavior. But sometimes, simply being able to do something tens of thousands of times faster or tens of thousands of times more cheaply is enough of a difference to require new rules, new moral frameworks, new modes of thinking.
"The computer is just doing what a human could do" simply isn't a compelling enough argument, any more than "the printing press is just doing what a scribe could do" would be.