Bad is having a moral lapse now and then while evil is total nihilistic immorality. Bad is mildly negative while evil is negativity of the most banal order. A bad person has moments of remorse & guilt whereas an evil person does not have a scintilla of remorse & guilt. An evil person in other words can be described in more modern, sophisticated terms as a sociopath, even a psychopath.
Bad is committing a venial sin which is forgivable while evil is committing a mortal sin which is damnable. Bad is moderate while evil is to the extreme. A bad person may make a prejudicial remark about a group of people while an evil person may put an entire group of people in a concentration camp. Bad may or may not be accidental in intent but evil is always intentional & never an accident. Evil knows what it is doing, it is purposeful in scope.
One can say that evil is a higher degree of bad. It also can be classified as beyond bad and into acts & actions of dissolution, even debauchery. Bad is having a low consciousness level while evil is zero levels of consciousness into the negative.