zajęcia is more less "classes, lessons" in this context, ussually in higher education or outside education, lessons are lekcje in school.
kurs is a set of classes, with a goal. like a Kurs nauki jazdy (driving learning course) is aimed to teach you to pass a driving licence exam.
zajęcia is also any activities.
In relation to this sentence, a teacher can use I invite you for my lessons and for my course interchangeably, if you have to attend classes to finish course , and to take course to go to the classes.