Fuck you, Lowtax. You're dead.
Actual content for anyone curious:
Emulation = Software Emulation - This is a program that runs in a host environment and tries to act like an old video game system. It is cheap and most emulators are pretty good nowadays, but it's not strictly accurate with regards to timing and stuff, and super accurate emulators are resource intensive. There is sometimes a perceptible delay between user input and something happening on screen as user input has to work through several layers of software. Examples - Chinese handhelds, Retroarch, SNES9X, Retropie on Raspberry Pi
FPGA = Hardware Emulation - Uses a piece of hardware that can be programmed to act like another piece of hardware. While bugs and inaccuracies are not impossible, it's generally more accurate than software emulation. These type of products have been gaining a lot of popularity in recent years. Products made using an FPGA are usually put together using a bit more care and are usually higher quality, and are aimed at enthusiasts as opposed to the cheaper emulation devices. There is usually no perceptible input delay as there is less software between the user input and hardware. Examples - Mister FPGA, Analouge Pocket/Super/Mega, Modretro Chromatic, The FPGA NES programmed into Everdrive 64.
System on a chip- A recreation of the original hardware using modern versions of the same components all crammed onto a little chip. NES Systems on a chip are often riddled with sound errors, but Super Nintendo and Genesis are usually OK. Usually more accurate in terms of timing than emulation, but usually the color and sound are a little off. All that being said, these vary in quality and there are some notoriously shitty NES SOCs out there. There is usually no input delay as there is virtually no software between the user input and hardware. Examples - Many systems made by Hyperkin & Retro-bit such as the RetroN 3 HD and the Super Retro Trio, GB Boy Color, many many little handheld and boxes that come with 500 NES games from China.
Out of these three, FPGAs has emerged as the premium option and where most acknowledge the future of the hobby heading. SOCs are basically dead, and emulation has been delegated to cheap chink shit, phones and PCs.
There are also systems that can play games from other systems natively.- These are systems whose hardware is so similar to an older system, it can execute the older systems code on bare hardware with a compatibility layer. This is different than all of the above and is generally going to be the most accurate. Examples include GBA games on 3DS, PS1 games on PSP and Gamecube Games on Wii & Wii U.