First off, it is an expense and you use Vendor Bills and Pay Bills for expenses. Invoices are for Customers and Income, despite the fact that negative income is an expense and you would have had to create a negative invoice.
As far as differences between accrual and cash, it is correct the way you have entered it. Ordinary expense (which is how you listed it) under cash rules is only an expense when paid, not billed. Actual Payroll Liabilities are different and Gross Wage plus incurred employer taxes are posted cash or accrual on day of payroll.
Use the steps found in this article on how to record your third party payroll through journal entries so that it posts wages correctly as an expense for the date of payroll.
https://quickbooks.intuit.com/learn-support/en-us/journal-entries/manually-enter-payroll-paychecks-i...
Use the info from your payroll report to create the journal entry. If you paid multiple employees for the pay period, you can combine all of their paycheck totals into one journal entry. You can also create separate journal entries for each employee if you need to break out the details.
