Simulation has different meanings in different industries

In electronic design, they use "time simulation" (or "dynamic simulation"), which is an off-line calculation of how a system might respond to various inputs. The inputs are mathematical in this case, and the simulation need not run in real-time. Indeed, in the old days it might take days of calculation to get the result, even if the real process was very brief. In electronics, these are termed "SPICE models". My work long ago with CSMP and analog computers was similar. Calculating physics events like nuclear or chemical reactions, or weather models is similar.

The other type is "real-time, hardware in the loop" simulation. Ideally, this is a "black box simulator' which can replace the actual "plant" and respond to the control system the same way the real plant will. Of course, this can be very cumbersome to realize, since all physical wires would have to be swapped between the actual plant and the simulator. Also, the electrical loadings of the simulator could be different. In practice, one often substitutes calculated inputs instead of real voltages from a black box. Many PLC's make this fairly easy.

In the "hydro proof" simulator I last worked on, we have a separate "black box" which reads analog voltages and outputs analog voltages representing the plant's sensor readings. However, it is permanently wired to the control PLC. The PLC has a switch (digital input) which selects either a simulation run or a real run, to look at either the black box output or the real signal. However, in most cases, black box simulations would only be done during initial commissioning. One does the best simulations you can, given practical constraints. Even using a black box simulator, you can get bitten. In my last case, even though we had the real control valve in the loop (with the stem moving), it responded differently in the actual run since line pressure on the valve plug pushed it open more than during the simulation (no line pressure). We had to add that effect to our model.