Research confuses me: what is the difference between case-control and cohort studies in quantitative research?

What is the difference between a cohort and a case-control trial? And why is it important? As a student, it is sometimes difficult to appreciate the difference between these two study methods, and why should it matter to us anyway? After all, we study medicine to treat patients, not statistics. Study methodologies were for the scientists; we are clinicians. Fast forward to clinical practice, and the importance of research design becomes apparent. As medical doctors we treat patients, but we also look at the bigger picture: why is this happening to this patient? Why is this patient more likely to be affected than another? In order to truly care for patients it is necessary to search and query and that means doing, or being able to properly interpret, research.