We know from electrostatics that the field of an infinite sheet of surface charge density $\sigma$ is
$$ \vec E = \frac{\sigma}{2\epsilon}\hat{x} $$
But the field inside the capacitor is
$$ \vec E = \frac{\sigma}{\epsilon}\hat{x} $$
That, in my understanding, is due to the addition of positive and negative plates fields
However in any other geometry such as a cylindrical geometry, we use the field due to one plate only. For instance, the following:
The E field is identical to that of only one plate, not the addition of the positive and negative plates fields. Why is this the case?