There is a difference. But the more alike two processes are in their input-output behavior, the more likely it is those processes are alike on the inside as well. If process B matches the input-output behavior of process A, it's imitating process A. If it is following an equivalent sequence of steps in order to generate those outputs, it's simulating process A.

The harder it is to discriminate between A and B on a long series of diverse inputs, the more likely it is that A and B are internally equivalent, not just externally similar. The reason is that there's no better fit than B = A.

I'm increasingly doubting whether my own brain might not, internally, use something that is architecturally similar to an LLM in order to compose comments like the one I'm writing now.