Payroll have two parts
1st one is earnings (basing on actual attendance how much one employee gets - Basic pay, DA, HRA & Allowances etc., PF & ESI documentation also includes under HR)
2nd one is deductions (PF, ESI, Prof. Tax, TDS, recovery of loans etc)
Usually, earnings part covered under HR and Deductions part covered under Finance.
But in small companies where there is no specific HR department, Finance people will look after total payroll.
Thanks
VIJAY