Identical behavior, sure, but much less overhead and fewer restrictions on e.g. resolution than you'd get on a general purpose emulator

The magic is that now you can modify the source code of the game and recompile that.

Folks have been optimizing SuperMario64 to run much faster on actual N64 hardware. And, there is a project that has ported it to run on the PlayStation 1. That’s much weaker hardware that has no hope of emulating the N64.