Compatibility is how well an emulator produces the same output as the original system when running a particular known program. Accuracy refers to how well an emulator produces the same output as the original system when running an arbitrary unknown program. An emulator can be highly compatible without being very accurate; NESticle was this way back in the 1990s, running a wide selection of popular North American commercial games.
In many cases, an emulator is more forgiving than the hardware, especially in when a program is allowed to write to a register. NESticle, for instance, allowed writes to $2007 at any time, when the NES allows it only on or after line 241 of each frame (vertical blanking) or when $2001 & $1E == 0 (forced blanking). Most emulators allow the program to twiddle PPU registers immediately, while the NES PPU ignores most writes for the first frame after a reset. Inaccuracies like these led to inadvertent development of programs that the NES itself cannot run during the early years of NES homebrew.
Whenever you discover a difference in behavior between the NES and best-of-breed emulators (like Nintendulator and Nestopia), you can help emulators become more accurate. First reduce your program to a minimal test case: keep removing things while the program continues to exhibit this difference. Then characterize the behavior difference as best you can and add it to the test suite.
Some emulators attempt to enhance the games to make them appear more appealing than they did on the original NES.
- Emulator tests
- Tricky-to-emulate games
- Game bugs - Accurate emulation should correctly reproduce known software bugs.
- Program compatibility - Homebrew games that may suffer from compatibility problems.
- Measuring an arbitrary emulator's accuracy reduces to the halting problem over linear bounded automata, which is intractable. It'd be easier to formally prove equivalence to the netlist of Visual 2A03 and 2C02.