A terminal emulator is a program that runs on a computer - now usually a personal computer such as a laptop or desktop - which allows the machine to emulate an old terminal, usually a video terminal. The computer on which the emulator is running is usually one which has an asynchronous serial line port, although on personal computers now, those are often provided by a USB device plugged into them, since serial ports are usually no longer standard equipment on them.
The suggested term "terminal simulator" means software and/or hardware that models some terminal down to hardware detail level. This category of technology has not yet been widely explored, but e.g. there are simulators that run the VT100 ROM rather than just mimic the effect of the control codes.