In American English usually a syllabus is a single short document (maybe 1-3 pages). It states the topics in the class, requirements, grading rules/expectations, who the instructors are, and the course schedule. For a single class, the curriculum is all of the teaching/learning content of the class. What topics are taught, what assignments are given, homework, readings, notes/slides/lectures, exams, etc. It is the overall structure of what students will learn and how they will learn it. A curriculum can also cover many classes in a sequence and that kind of curriculum is about how the classes connect and fit together to be a complete experience for a student who takes the sequence of classes.

A curriculum is the course and a syllabus is the topic. http://learnersdictionary.com/definition/curriculum http://learnersdictionary.com/definition/syllabus

They are usually used interchangeably in conversation. In reality, a syllabus will typically describe the requirements of a subject, while a curriculum covers the requirements of an entire course of study. For example a 7th grade science class could have an overall curriculum and an astronomy syllabus. I don't usually see anyone note this distinction however.