The Domain Registrar is where it all starts. The Registrar is the organization where your domain is sourced (if available!) and ownership is established. They can register and create top-level domains such as .com, .ca, .net, etc. The Domain Registrar creates the domain, (ie. mycompany.ca) establishes the registration and technical contact information (this can be hidden) and points the domain name to a Domain Name Server(s). As a small business owner, you should make efforts to ensure you own the registration record.
The Domain Name System and Records
The Domain Name System (or DNS for short) creates name records (ie. mycompany.ca) which are the labels applied to a specific IP Address. Your domain will have many different DNS records which point to various items such as email, websites, etc.
The IP Address
Each DNS record leads to a specific IP address (ie 192.168.0.1). This would be called a Host, which is where a program or service lives relative to your domain. If you wanted to move your website to a new Host, you would merely change the DNS record for mycompany.ca to point at a new Host.
I recommend that clients have direct access to the Registrar and DNS management of their organizations domain. Often IT providers will group clients domain information into a single account for ease of management which is great for them, but not so great for you if you ever decide to move on or need to have another party deal with your web presence.
When dealing with your website, email, registrar and DNS hosting you often may be dealing with different companies. You should have a clear understanding of who these companies are and how their services are maintained and billed.