Access to change employee hours has been setup under the Budgets menu: Edit ST OT Hours. This functionality give Managers access to edit hours. In order to make changes other than hours and for all changes on the Payroll Assignments screen the person would need permission to the Payroll module.
The overall difference between Payroll Assignments and the Hourly Staffing is that employee/group of employees pay on Payroll Assignments screen is pay is entered as a single amount which can then be managed to a overall percentage by month ($50,000 base * 0.75 per month = $37,500 for the year).
If you wish to allocate an employee/group of employees to various projects based on days or schedule you should the Hourly Staffing schedule. On the Hourly Staffing screen pay is entered as an hourly amount and the total pay is the hourly amount * the number of hours worked per pay period (eg $10 per hour * 5 hours per week * 52 weeks = $2600). Both straight hours and overtime hours can be entered by pay period. The Hourly Staffing schedule is user-defined and allows for up to 53 pay periods.