the federal is the US income tax. is one that goes to the IRS on which you report your worldwide income with certain exceptions. generally, the income tax rates are higher than for the state. your resident state evidently also taxes you income, as stated its rates are lower. so taxpayers residing in a state with an income tax pay taxes to both.
The IRS and state taxing agencies are different taxing agencies as well. They both operate independently of each other. The tax rates used on your federal income tax rate will different from the tax rate used on your state tax return.
Also, they may utilize different deductions. The federal tax return may use the standard deduction while you are able to itemize deductions on your state tax return. This could result in a lower taxable income on your state income tax return.
Also many states offer credits that are not available on the federal tax returns.
Essentially there are many factors that come into play when trying to determine the difference between the federal and state income taxes.
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