Users need to be careful when downloading emulators and ROMs since it is possible for a virus or malware to pretend to be either one of these things. However, they also tend to run slower than the device they're mimicking since they're reproducing a behavior rather than having been built for it. Emulators can be very helpful for game preservation and allow you to run apps you usually couldn't on the device that hosts them. Only do so if you know what you are doing and are ok with the possible consequences. Users often need to jailbreak their iOS device in order to run emulators and ROMs, which can open the device to some security risks.
So, you can think of the emulator as a digital console while the ROM is a digital game. A ROM is the downloadable version of the game necessary for playing said game. The second half of an emulator is the ROMs.
For example, a PSP emulator mimics the PSP and can play compatible PSP games on whatever device it is on. An emulator is a device or program that imitates another computer or program.