Is there a difference between the owner of a domain and the manager of the DNS?"
That is a good question and yes there is a difference.
When a business or individual wishes to obtain a domain name they will register or purchase the domain (providing that it is not already in use) with an authorised domain name registrar such as Melbourne IT, Godaddy, Crazy Domains etc
The business/individual who successfully registers the domain name becomes the owner of that domain name.
Being the owner of a domain allows the owner to either manage the DNS for the domain, or delegate the management of DNS to some other 3rd party.
This means that the domain owner can also be the manager of DNS for that domain, or the domain owner may have delegated management to someone else for DNS.
A 3rd party that manages DNS for a domain owner will in most cases have no ability to manage the domain name for the domain owner.
What is a DNS?
For information on what a DNS is, please see this helpful link