A domain is your site's address (yourcompany.com), hosting is the server where its files live, and DNS is the system that translates the domain into that server's address. Three separate services, often from three different providers – and it pays to know who controls which.
An analogy: the domain is the sign with your address, hosting is the premises, and DNS is the address book that directs visitors to the right door. This separation is what lets you move a site to different hosting without changing the address: update the DNS records and the world still arrives at yourcompany.com.
The practical minimum for a business owner: the domain registered to the company (not to an agency or "the IT person who once helped"), registrar panel access in company hands, auto-renewal switched on. An expired domain means your website and email disappear on the same day.
Warning sign: if the domain or the hosting account is registered to your vendor, every change of supplier becomes a negotiation. Sorting out domain ownership costs an hour of work; recovering it from a fallen-out vendor can cost months.