No. They are different.
Payroll - the records about wages paid to employees that business keeps. Used to be an actual 'roll' or ledger with amounts recorded. You have a general ledger, accounts payable, payroll, etc. for a business.
Payroll - the act of paying wages, etc. for a single pay period. Example: "Have you run the payroll yet, Ms. Accountant?"
Payslip - the single record given to an individual employee outlining what they got paid, tax, entitlments, etc. for a single pay period. Example: "Can I have my payslip, Ms. Accountant? I want to see how much tax you have taken from my gross pay."
Does that help? IT Nerds rule by the way
And perhaps you should just buy MYOB...