What is the difference between an administrator and a contact?

Short answer: A contact is someone who has interacted with the shop, or whom an administrator added to the account's contact list; an administrator is someone who can get into your dashboard. Every administrator is also a contact, but not the other way round.

These are the people who have interacted with the shop, or whom an administrator added to the account's contact list — by an import or by hand. They never get into the dashboard, and only have access to the shop.

These are the people you invited to run the account with you. Each of them also has a contact profile: in the contacts list, a chip shows their role — Admin when they have no other.

When you type an email address into the invitation, your existing contacts are suggested. Picking one attaches the access to their profile instead of creating a second one.