What is the difference between being an Owner and an Administrator?

While administrators can also have approval and billing permissions, the owner will have these permissions assigned automatically, and they can't be revoked. Note that the owner can always override the administrators' changes. The owner is the one that is responsible for the account legally - their name will appear on the invoice as a reference. 

Owners are the only ones who can enable the Public Images feature for all users and control the explicitness level of the public images.

Read more about user types and permissions here: https://www.pickit.com/help/what-different-kinds-of-user-types-are-there