When a Platform Manager selects "give parental access," users are given the parent role regardless of the actual relationship to the student (i.e., aunt, grandparent) and they have access to student information that is published to parents. They are also included as parents in lists, reports, mailing labels, etc.
When a Platform Manager selects "list as parent," users are only listed as the student's parent in reports, lists, and mail labels, but will not have access to the student's information such as courses, report cards, etc.
See the article, How do I grant or edit parental access? for more information on how to set up Parental Access.