If a patient or their injury or illness is responding to treatment, the treatment is working and they are getting better. I'm pleased to say that he is now doing well and responding to treatment
When you respond to a need, crisis, or challenge, you take the necessary or appropriate action. This modest group size allows our teachers to respond to the needs of each student. = react
When you respond to something that is done or said, you react to it by doing or saying something yourself. They are likely to respond positively to the President's request for aid The army responded with gunfire and tear gas `Are you well enough to carry on? --- `Of course,' she responded scornfully The Belgian Minister of Foreign Affairs responded that the protection of refugees was a matter for an international organization