The two terms are often used interchangeably.
Course registration is the process to register for a course or as a student at a university.
Course enrolment is used more frequently for after someone has registered or the rules for registering... BUT enrolment is also used to sign-up or register.
EX. The course enrolment is limited to 50 students. Only 50 students can take the class.
The professor checked to see how many students were enrolled in his class but only 25 had registered/enrolled.