A program that can produce copies is the same as a copy. How that copy comes into being (whether out of an algorithm or read from a support) is related, but not relevant.
A program that always produces copies is the same as a copy. A program that merely can produce copies categorically is not.
The Library of Babel[1] can produce copyrighted works, and for that matter so can any random number generator, but in almost every normal circumstance will not. The same is true for LLMs and diffusion models. While there are some circumstance that you can produce copies of a work, in natural use that's only for things that will come up thousands of times in its training set -- by and large, famous works in the public domain, or cultural touch-stones so iconic that they're essentially genericized (one main copyrighted example are the officially released promo materials for movies).