Net Income
Net income is the pay that reaches your bank account after taxes and other deductions. For an employee it is the deposit amount on the pay stub. For a self-employed person it is business revenue minus expenses, the net profit reported on a tax return.
Most landlords do not use net income for the 3x rent rule, but some do, and the difference changes the answer. Three times a $1,500 rent in take-home pay means $4,500 deposited every month, which takes a salary well above the $54,000 that passes on a gross basis.
Net income matters more for your own budget than for the application. Rent is paid from take-home pay, so a renter who clears 3x gross should still check the rent against the net figure. See gross vs net income.