Input offset voltage varies with ambient temperature and operational amplifier common-mode input voltage. It also varies over time.

The differences between how input offset voltage is corrected in a zero-drift operational amplifier versus how it is corrected in a regular high-accuracy operational amplifier are reflected in their output voltage characteristics.
An example comparing results using an amplifier circuit configured using a gain of 225 times is provided below.

1. Temperature Dependency

The graph below indicates the temperature characteristics relative to output voltage error (deviation from REF voltage) at VDD=5V and IDET=0A.

The input offset voltage of a regular high-accuracy operational amplifier is trimmed and corrected to minimize the output voltage error at 25°C, but temperature fluctuations may change the input offset voltage and cause the output voltage error to rise.
A zero-drift operational amplifier, however, automatically corrects the input offset voltage and even if temperature changes cause the input offset voltage to change, the input offset voltage can at all times be minimized to lower the output voltage error.

2. Common-mode Input Voltage Dependency

The graph below indicates the common-mode input voltage dependency of output voltage error (deviation from REF voltage) at VDD=4.5 to 5.5V, IDET=0A.

The input voltage of an operational amplifier is fixed, but changes in VDD will change the common-mode input voltage as seen from VDD.

While the output voltage error of a regular high-accuracy operational amplifier is minimized under common-mode input voltage conditions where the input offset voltage is trimmed and corrected, changes in the input offset voltage due to fluctuations in the common-mode input voltage will cause the output voltage error to rise.
On the other hand, a zero-drift operational amplifier can automatically correct the input offset voltage. Thus, even if the input offset voltage changes due to a change in the common-mode input voltage, the operational amplifier will at all times be able to minimize the input offset voltage to keep the output voltage error low.

As stated above, a zero-drift operational amplifier will be able to minimize the input offset voltage at all times without being impacted by fluctuations in ambient temperature or common-mode input voltage to maintain a low output voltage error.
The output voltage error can be kept small even when the input offset voltage changes over time.