These three items are on a spectrum. In the prototype you have a physical circuit that works in the physical world.
On the opposite spectrum end is a simulation. You get a mathematical output of tabulated numbers or a graph. If it is a time domain analysis the computer time taken for the calculations may be different than the real world time simulated.
In the midddle is emulation. This is a hybrid of the two. One example is from the early days of microprocessors. There were computer programs with built in diagnostics that had the same function as a microprocessor. There was an interface cable from the compuer which had a plug that would fit into a PC card socket for the microprocessor to be emulated. The external PC card and circuitry would run as if there were a real microprocessor in the socket. The human could interface with the computer program diagnostics to find errors in the code stored on the PC card ROM.