You have it exactly back asswards.
A simulator simulates how and emulator emulates what.
If I develop an exact description of the hardware down to the individual registers and control paths, that is called a simulator.
Ah, I see, when I control a virtual airplane the program is behind the scenes calculating all the mechanical, electrical, and {aero,hydro}dynamical forces, from the engine, from the control cables, from the landing gear, from everything, all the time, so we can call it a flight simulator. Oh wait, it doesn't! It just makes a rough estimate of the aerodynamical forces, to what you would expect it to behave. Then according to your (wrong) definition, we should call it a flight emulator.