Operational amplifier basics
The differential voltage is only zero in an ideal world. It is a useful approximation in modeling operational amplifier circuits. Consider, for example, a simple operational amplifier circuit with a gain of 100.  If the input voltage is 10 millivolts, the output voltage will be 100 times greater or 1 volt. Assume that the open loop gain of the operational amplifier is 100,000.  That means that the voltage across its inputs would be 1 volt/100,000 or 10 microvolts which is 1000 times smaller than the input voltage.  Under those conditions, it is reasonable to model the differential voltage as zero.