No. Stimulus checks are advances of refundable credits on your tax return. They are not taxable income. They will not raise your tax or lower your refund.
A disaster distribution is from a retirement account (IRA, 401k for example) and is taxable income. You will get a form 1099-R showing distributions which you will use to report that income. After entering the form 1099-R information you will be asked a series of questions to determine if the distribution meets the criteria to be treated as a disaster distribution. If qualified as a disaster distribution any early withdrawal penalties are waived and one can spread the tax on the distribution income over 3 years.
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