Payroll Giving (sometimes referred to as Give As You Earn (GAYE)) is a way of giving money to charity through your employer pre-tax (but after National Insurance). The amount of tax relief you get depends on the rate of tax you pay but it is particularly cost effective for higher rate taxpayers.
Your employer needs to set up and run the scheme which involves making deductions each time they run payroll. The donation will be taken from employees’ pay before tax but after National Insurance.
The donations are then sent to a Payroll Giving agency who then pass them on to the chosen charities.
You earn £60,000 per year (making your marginal tax band 40%). You donate £1,500 through payroll giving. Your take-home pay only reduces by £900. (From £43,849.40 to £42,949.40, assuming no other deductions).
Gift Aid
You earn £60,000 per year (making your marginal tax band 40%). You donate £1,200 to a charity after you've been paid. The charity can claim 25% from the government, giving them £1,500. And you can claim a tax rebate of £300 (1500 * 0.2), meaning you are only out-of-pocket £900.
Comparison
Both benefit you and the charity the same
Both reduce your 'income' for the purposes of tax
With Gift Aid, the charity needs to take the step of actually making the claim from the government for the 25% top up.
With Gift Aid, you need to go through the step of claiming your tax rebate, including keeping track of how much you have donated throughout the year.