Schoolwork is work assigned by a teacher, school, or other educational institution. The term generally refers to both work completed at home (homework), as well as work completed during class (classwork). Typically, schoolwork is done in class, during the time period allotted by the instructor. However, it may be reassigned as homework, in which case it is done outside of the class.
In fact, schoolwork is very similar to homework. It is usually up to the teacher's discretion when assignments are to be completed, and often work that is not finished during class will be assigned as extra homework.
By a broad definition, schoolwork can be extended to refer to any academic activities at school, and would therefore include exams, tests, and quizzes as well as the normal type of work.
Unlike schoolwork, coursework generally refers to the more advanced work done in college. Coursework is the assignments that are assigned by the professor and many require anything from reading to completing projects.