In my opinion, these are different errors that do not depend on each other.
Voff is a result of the difference between the characteristics of the two transistors building the differential pair.
The common-mode voltage error is a result of the imperfections of the current source in the emitters.
We can say that the offset voltage is an additive (constant) imperfection while the output voltage caused by the common-mode voltage is a multiplicative (proportional) error.
It is caused by the fact that the output of the differential stage is single-ended (only one of the two collector voltages is taken as the output). If the output was differential (both collector voltages were used as output), there would be no such error because they would change in the same manner and their difference would always be zero.
Strictly speaking, the non-inverting amplifier does not represent a "true" common mode since the second input voltage (applied to the inverting input) is not exactly equal to the first input voltage (applied to the non-inverting input)... and, as
@jp314 noted, it is proportional to the op-amp output voltage.
You can observe a "true" common mode if, for example, you join the two inputs of a differential stage and apply a single input voltage to them.
If you want, I can illustrate my explanations with a circuit diagram.