The tax on your gambling winnings is not calculated separately from your other income. On your tax return, all your income is added up and the tax for the year is calculated on your total income. The amount that's calculated on your tax return is the tax that you actually pay on your total income.
The tax that you had withheld from your winnings is an advance payment towards the total tax that's calculated on your tax return. It is not specifically tax on the winnings. The total tax withheld during the year, from all income sources, is applied to the total tax calculated on your tax return. If the tax that was withheld is more than your actual tax, you get a refund of the overpayment. If the tax withheld is less than your actual total tax, you have to pay the difference.
