I would add to Martin's very informative answer by suggesting that you don't use the words prospective and retrospective. The give the wrong idea. Prospective gives the idea that you are starting from today, and retrospective gives the idea that you are looking at data that already have been collected.

In fact, as Martin points out, prospective means that we measure the risk factors and then follow forward to look at incidence of endpoints - something that we can perfectly well do with data that have been already collected, such as hospital charts or occupational health data. In a retrospective study, we start with the disease – either present or absent – and look back to determine exposure to risk. This too can either be done de novo or by using existing information.

The terms cohort and case-control are unambiguous. They describe the study design. I would stick with them. In fact, in my courses I have banned the terms prospective and retrospective, along with type I and II error (false positive and false negative error are much better terms).

A retrospective cohort study is a cohort study and not a case-control study. The cohort study allows to determine incidences  of disease among cohorts while a case-control study allows only to determine percentages of exposure among cases and controls.The term "retrospective" gives information about chronology of data collection. A case-control study may be a prospective study.