The common definition of the input common-mode voltage range (CMVR) for operational amplifiers (Op-Amps) is the average voltage of the inverting and non-inverting input voltages. This is acceptable for op amps because they use negative feedback and usually stay within 1 mV between inputs.
It is rare for a comparator to have an input voltage value that is so close. Most use cases for comparators have large differences between the input pins. Although the average value of the two inputs may be within the common mode range, the value of one of a comparator’s inputs may exceed the input range specification.
As an example, consider a comparator with an input voltage limit of 3.5V. One input is a 4V DC signal and the other is a 2V DC signal. Under the definition of operational amplifier, the input is valid and the average is 3V. However, this is a violation because both input voltages must be lower than 3.5V, and the 4V signal violates the input range specification.
The absolute maximum input voltage range for a comparator specifies the voltage range where the input will remain undamaged and performance is not guaranteed when it exceeds the specified input working range.
In conclusion, the input common-mode voltage range specifies the voltage range of each input to ensure normal operation of the device. Do not “average” the input voltage of a comparator.
Below is a snippet from a Texas Instruments presentation summarizing the common mode range in a comparator.