A tax credit cuts the tax itself. A tax deduction cuts the income the tax is calculated on. Same dollar amount, different line, different result. One is a subtraction from the bill. The other is a subtraction from the number the bill is based on.

The IRS puts it in those terms. A credit reduces the income tax owed, dollar for dollar, based on the return. A deduction reduces income before the tax is figured. That is the whole distinction. The rest is where each one sits on Form 1040, and what happens if the credit is larger than the tax.
The IRS’s own arithmetic
The IRS teaching example uses a 15 percent rate and a $200 item. Treat the numbers as a labeled hypothetical, not a filing position.

Start with $10,000 of income subject to tax. Tax at 15 percent is $1,500. A $200 deduction lowers income subject to tax to $9,800. Tax at the same rate is $1,470. The deduction saved $30 — the $200 times the 15 percent rate. A $200 credit, applied to the $1,500 bill, leaves $1,300. The credit saved $200.
That is why a credit and a deduction with the same face amount are not interchangeable. The credit hits the tax. The deduction hits the base. The value of the deduction moves with the rate that applies to the last dollar of taxable income. The value of a credit that you can actually use is the face amount, until the bill hits zero.

Refundable, nonrefundable, and leftover amounts
Some credits are refundable. If the tax is smaller than the credit, the difference can come back in the refund. The Earned Income Tax Credit is the example the IRS uses. Some people who are not otherwise required to file still file in order to claim a refundable credit.

A nonrefundable credit stops at zero tax. Leftover amount does not become a refund. The Child Tax Credit, in the IRS’s current individual-credit explainer, is described that way: it reduces liability. Other credits are mixed. The American Opportunity Tax Credit is partly refundable under published rules. Which credits exist, and how much of each is refundable, changes by tax year.

None of that is an eligibility decision for a household. The tests sit in the current-year instructions and publications.
Deductions have a fork
Most people take the standard deduction: a published dollar amount that reduces taxable income. The IRS adjusts it for inflation. The amount depends on filing status, age, blindness, and whether someone else can claim the taxpayer as a dependent.

Some people itemize on Schedule A instead — medical expenses, certain taxes, interest, charitable contributions, and other listed items. You cannot take the standard deduction if you itemize. A few filers must itemize. In most other cases the mechanical comparison is which number is larger. That is a description of the form, not a choice for one household.
Some deductions come off before adjusted gross income. Those are a different line from the standard-or-itemize choice. They still reduce income, not tax. They still are not credits.

Statutes and IRS publications change. Confirm the current text at the agency that issues it.