It’s fundamentally extremely comparable mathematically and algorithmically. That’s the point. Simulated annealing doesn’t need to understand the search space to find a pretty good answer to a problem. It just needs to know what a good answer approximately looks like and nudge potential answers closer that way.
What LLMs are doing is not mysterious at all. Why a specific point in a model is what it is is, but there’s no mystery to the algorithm. We can’t even guess at most of the algorithms that make up the brain.