This difference between formal lessons and audited lessons exists also in other places, and other fields of study. The difference has to do partly with accreditation/prerequisite status. Formal lessons includes testing and recognized accreditation if passing tests, that will be recognized for further lessons or more advanced courses, and other teachers. Auditing lessons/attending for personal interest/improvement doesn't carry any recognized accreditation, has no tests. It is obviously worth something, but has a different status. Some kind of gifts of appreciation would seem to fill the bill, perhaps? For some kinds of auditing of lessons, payment is required.