Interdiscipline -- usually called interdisciplinary -- is a concept in academia in which a study, class or other body of information incorporates subject matter and research from multiple academic disciplines. For example, businesses use psychology for human relations. Therefore, a study covering psychology in the workplace would be an interdisciplinary study covering both the psychology and business.
Sub-disciplines are the opposite. A sub-discipline is a subcategory of a broader category. In English literature, British literature and American literature are sub-disciplines of literature. Academics tend to specialize in specific disciplines, allowing them to understand discipline more thoroughly, market themselves as experts in the field and more easily publish on a specific topic. Academics can further specialize within a sub-discipline. For example, a British literature specialist can focus on the works of Virginia Woolf.
Subjects are often grouped into categories so that universities or other organizations can create departments. For example, literature, writing, grammar and philosophy are often grouped into the English category and biology, chemistry, physics, astronomy and geology are grouped into the science category. These disciplines could be seen as sub-disciplines of the broader categories.
Some subjects inevitably overlap with other subjects. Each area of expertise can require much background knowledge and a certain cognitive orientation. For example, researchers in the humanities place more emphasis on interpretation, while researchers in the hard sciences place more emphasis on collecting empirical data from scientific experiments. When isolated, sub-disciplines provide a more limited scope.
Schools sometimes have instructors from different disciplines team-teach a class, allowing experts from different specializations to bring their unique perspectives to a single topic. For example, a history instructor and an English instructor could teach a class titled The Enlightenment on English Literature. The history teacher would cover the historical background and the English teacher would cover the literature. In contrast, schools also have instructors teach highly specialized sub-disciplinary courses. The instructor who specializes in the writings of Virginia Woolf could offer a course that focuses exclusively on her, allowing the instructor to bring his highly specialized knowledge of Woolf to the students.