There is no difference between a tax write-off and a tax deduction. It's possible that the confusion arises between a tax credit and a tax deduction; a credit subtracts an amount from a person's tax liabilities, while a deduction is a qualifying expense that reduces the amount of income that can be taxed.

Tax Credits

A tax credit allows the person who qualifies for the credit to have that amount either reduce his tax liability or increases his tax return, depending how much he has paid in taxes throughout the fiscal year.

The child tax credit is the most well-known tax credit. If a person has a child who qualifies for the child tax credit, that person can receive a credit of up to $1,000 per child. If a person with a qualifying child owes $3,000 in taxes at the end of the year, he can apply the child tax credit and would then only owe $2,000 in taxes.

If the same person with a qualifying child received a refund of $1,000, the tax credit would increase his refund to $2,000.

Tax Deductions

Unlike a tax credit, a tax deduction reduces the amount of income that can be taxed.

For example, if a person acts as a sole proprietor, many of his business expenses can be claimed as deductions. Office expenses such as rent would be considered tax deductions and would reduce the amount of taxable income he earned.
If the person earned $100 in his business over the course of a fiscal year but paid $25 in office rent, the total taxable income would be $75, which would reduce the amount of taxes owed.