My client is certain that they have, in the past, initiated credit card refunds from within CiviCRM, such that it triggers an actual refund of the credit card payment to the cardholder.
In contrast, in their current setup, using Stripe, they must initiate the refund within their Stripe console at stripe.com and then ensure the refund is properly recorded in CiviCRM.
For which payment processors (Authorize.net, iATS, etc.), if any, would a staff user be able to initiate the refund process from within CiviCRM, without needing to separately initiate the refund in their payment processor terminal/console?