In general, any mechanism fits any door. If you go back far enough, that’s not true, but it’s true for ’70s and newer games.
Bob Roberts has some good advice on coin mechanisms.
Cutter mechanisms have internal blades that cut strings, from the good old days where kids would drill a hole in a quarter and attach a string. The cutter mechanisms ensured that the operator got his quarter, even if the kid got his game.
This doesn’t matter much for collectors, but now you know!