It depends on the type of report and what you’re using the information for.
Time Card Reports
For time cards, you typically want to know the hours worked during the pay period, so using the pay period as the date range makes sense.
Payroll Reports, Tax Deposit, etc.
For reports, like the tax deposit, that need information from paychecks—you’ll want the date range to include the dates checks were actually issued (post date). Typically, this is at least one day after the pay period ended.
Pay Period = May 1 to May 15. Checks posted on May 16.
In the example above, when running a tax deposit for the pay period, use a date range that includes the post date of the paychecks. It could be for just one day (the 16th) or if you posted some checks later, on the 17th or 18th, the range could be from the 16th through the 18th.