A case study is an in-depth study or description of a person, place or an event. A case study is usually included in a writing to cite a detailed example of the topic being discussed. It is done to give readers a clearer picture and insight of the topic in general.
And when an author includes evidence in a case study, it is not to conduct an investigation or add a case or help the reader check the case study but to help the reader draw conclusion from the case study.
A plot is, basically, the events that make up a story or are part of a story. The plot can have very little to very many events. It's kind of like the storyline.