Are the same ?
See,I’m working on this software paycheck calculator
and I need to write a proper description,but the definition on my dictionary is not clear.
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.
or
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…
Perfect! Thanks a lot …
and yes,I’m a bit nerdy sometimes
FWIW - I assume you are working to Italian tax laws etc. given your location (which I have no idea about) but I’ve written payroll solutions here in the UK for a variety of accountants in several programming languages.
If you need any help on coding specifics just pm me.