The Delinquency Report is a report that will show the families who have balances in the month or months prior to the current month. 

The  Aging Report, when run to include accounts with current balances, will provide the exact and correct data of how much a family or families still owe in the current month. 

For example: If the current month (month when you are running the report) is June 2018, the Delinquency Report will show you data from May, 2018, April, 2018, March, 2018.    The Aging Report when run to include accounts with current balances, will provide you data on the month of June 2018 ... this will reflect any payments the parent has made that month.  So when you compare both reports, the Delinquency Report will show you data from May 2018 while the Aging Report will show you date on the month of June 2018.