WASHINGTON—In the second big wave of stimulus payments, the IRS will send money over the next few days to people who recently provided their direct-deposit information.

These payments will likely go to two groups: One set is tax filers who successfully used the Internal Revenue Service website’s “Get My Payment” tool to add bank information by midday on April 22, according to the IRS. The other set is people who don’t file tax returns but who receive Social Security or Social Security disability benefits, according to the...