A course is a class that you sign up for. It covers a specific topic and lasts for a specific period of time (one semester, for example) — "Art of the High Renaissance," or "Introduction to Photography". A subject is a general field of study — art history, chemistry, European history, etc. Sometimes they are synonyms, especially when you are talking in general about your classes: - I am taking five subjects this semester. / I am taking five courses this semester. - I failed every subject in my first semester / I failed every course in my first semester. In both of those sentences, "course" is more common.

A subject is more general. For example, you can take a 4 week course titled "Italian for beginners". The course is "Italian for beginners" The subject is Italian