A discrepancy is a lack of agreement or balance. If there is a discrepancy between the money you earned and the number on your paycheck, you should complain to your boss.
There is a discrepancy when there is a difference between two things that should be alike. For example, there can be a wide discrepancy or a slight discrepancy between two objects, stories, or facts. The noun discrepancy is from Latin discrepare "to sound differently," from the prefix dis- "from" plus crepare "to rattle, creak."