Can someone tell me how the vaccine mitigates the severe symptoms of Covid but not prevent the infection? I'm not a doctor but this sounds strange to me. If we are just preventing severe symptoms couldn't we do that after infection anyways, isn't that what we do anyway with other flus and such?

Can someone tell me how the vaccine mitigates the severe symptoms of Covid but not prevent the infection? I'm not a doctor but this sounds strange to me. If we are just preventing severs symptoms couldn't we do that after infection anyways, isn't that what we do anyway with other flus and such?