Opt Out of Marketing for Subscribers

Hi there, 

I was wondering what is the difference between someone opting out of marketing communications and unsubscribing from one of our mailing lists. 

For example, we have a general newsletter sign-up and we also have mailing lists created for courses that we run. Let's say a user has signed up for our newsletter but later decides they want to unsubscribe from our mailing list. Do we still have permission to send them marketing communications? Another scenario would be that a user belongs to our newsletter AND a course mailing list and they decide to unsubscribe from our newsletter. Can we still send them communications for the course mailing list that they are still subscribed to?

I would appreciate if anyone has any insights on this. I'm fairly new to this mailing process.

Thank you for your time.