You can have corners and monte-carlo for process as well as mismatch!
Yield is typical simulated by monte-carlo. Corner simulation verify if your circuit work up to specification in an unlikely process parameter corner.
The same approach is applicable to process mismatch. You can have a corner made of an individual instance or vary all relevant instances at all by distributions.
But I don't understand the last one.
I never run monte-carlo simulation at corners because this is not realistic at all. Can you please explain in a better way if I'm wrong ?