You can run an LLM locally (and distributed compile systems, where the compiler runs in the cloud, are a thing, too) so that doesn't really produce a distinction between the two.

Likewise, many optimization techniques involve some randomness, whether it's approximating an NP-thorny subproblem, or using PGO guided by statistical sampling. People might disable those in pursuit of reproducible builds, but no one would claim that enabling those features makes GCC or LLVM no longer a compiler. So nondeterminism isn't really the distinguishing factor either.