The variations on the parameters of the devices (Transistors, Resistors, Cap...) can be divided in two parts (I'll give the example for resistors):
-Systematic Variations: this is usually referred as Process variations - in this case ALL the resistors in the same lot suffer from the same variation. For example, in one lot you can have ALL the resistors 15 % above the typical value and, in another lot you may have ALL the resistors 10 % below the typ value.
The bottom line is "all the devices in the same lot suffer similar deviations in their parameters"
-Random deviations: These deviations are MUCH SMALLER than the previous ones an occur in equally drawn devices, even if they are very near each other. This depends on the area of the devices. For example you may make a layout in which two equally drawn resistors have (only) a random difference of, say, sigma(DeltaR/R)=0.1 %. This is what causes offset voltages in the circuits.
Your corner simulations must be done using the maximum systematic deviations and, then, if the offset voltages affect your circuit´s performance, you should make monte-carlo simulations.