Empirical study: Aims to gain new knowledge on a topic through direct or indirect observation and research. This type of article may use both quantitative or qualitative data and analysis. An empirical article will often include the following sections: Introduction, Methods, Results, and Discussion.
(Literature) Review article: This is a type of article that provides a synthesis of existing research on a particular topic. These are useful when you want to get an idea of a body of research that you are not yet familiar with. It differs from a systematic review in that it does not aim to capture ALL of the research on a particular topic.
Case Study: Often describes an unusual case or observation. It is common in medicine to report the occurrence of previously unknown or emerging disease. A case study paper usually examines a single subject of analysis, but case study papers can also be designed as a comparative investigation that shows relationships between two or among more than two subjects.
For more see:
Cornell University's Guide
Yale Journal of Biology and Medicine Guide
and Berkeley's University's useful glossary of science terminology