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A name server is a server that returns an IP address when given a domain name. This IP address is basically the domain's location on the Internet.
Sometimes name servers are referred as DNS servers (and vice versa) because they essentially perform the same function; when given a domain name, they return the IP address for that domain.
The difference is that with DNS, the domain owner will be setting the IP addresses to your domain and your mail server(s). For domains registered at Dynadot, you will be using the Dynadot servers, however, you will be setting up the IP addresses within your Dynadot account. If you are using name servers obtained from your web host, you are using your web host's servers, and they typically set up the IP addresses for you.
Basically, DNS is where you set the IP address for your domain while with name servers, your web host sets the IP address for you.
Find out how to set your domain's name servers.
Find out how to set up DNS for your domain.