A course description and a course syllabus are directed at two difference audiences. A course description is aimed at students who are not yet enrolled in the course. A course syllabus is for students who are already enrolled in the class. It is not written for people who are not enrolled in the course.
A course description is usually displayed in the course catalog and on the school website. It is public information for anyone to access. A course syllabus is given to students on the first day of class and is usually not displayed elsewhere, unless it is on the instructor's personal website.
A course description is a brief overview of the course and is just one paragraph long, usually less than 100 words. Some may be as short as a few sentences. A course syllabus is a comprehensive overview of the course. It is usually one or two pages long, but can span several pages depending on the content and length of the course.
The job of a course description is to inform prospective students on what a class entails, so they can decide if they want to enroll in the course. The job of the course syllabus is to inform students on important aspects of the class, including the instructor's name, the room number, the required list of materials and a detailed outline of what the course will cover. It may also include the instructor's policies on attendance and late work, as well as important deadlines and test dates.