A small employer may use a pay stub generator because it does not have a payroll department. A self-employed person may prepare an earnings statement to organize real income. Both uses can be legitimate when the hours, rates, payments, taxes, and business details are truthful.
The problem begins when someone changes or invents material information to influence a housing, credit, employment, insurance, or benefit decision.
Your guide to whether making your own pay stub is legal explains the basic difference: creating a record is not the same as falsifying one.