The ROM chips were literally lower specced / worse tolerances, and thus cheaper. FastROM chips were guaranteed (by the manufacturers) to yield stable results in under 120ns, versus 200 for SlowROM.
SNES emulation is extremely accurate at this point - any modern/reasonably competent emulator handles this correctly. Shoutout to Near (RIP) here - they wrote an article on Ars which documents how we've reached this point.
On top of this, most emulators allow you to run the game at faster speeds than the original. I haven't encountered a game yet where I wanted to do this, but the fact that it's available just shows how far emulation has come (and the wizardry that is involved in emulating an entire computer system).
Ostensibly the reason is that the ROM chips have to run in lockstep with the CPU clock, so the CPU may need to be downclocked if cheaper ROM chips can't keep up with it, but I don't know what the actual cost difference would have been at the time, if any. Maybe all of the chips were capable of 3.58mhz and Nintendo was just gouging.
