I’ve worked at my family’s grocery store from 9th to 12th grade without pay every summer. Would this count as work experience or would it go under volunteering?
Work.
Yes, this ‘work’ experience will be a major factor in helping the application readers to know how you’ve spent your time outside of the classroom.
I’d count it as work. Your labor was for a private, for-profit business, so I don’t see how it can be volunteering. If you want to get fancy you can call it an internship, but I would only do that if you were actively working on the professional/management side (i.e. purchasing, advertising, bookkeeping, etc. - not restocking shelves, cashiering, or bagging groceries).
This is definitely work. Also many kids who work in a family business have bigger responsibilities than those working for low wages. Make sure you describe all of your duties.