Are Domain Name Server and Name Server the same thing?

Solution 1:

There is no such thing as a Domain Name Server.

DNS stands for Domain Name System, which is simply a hierarchy of Name Servers that has the intent to translate host names into IP addresses on a global scale. A name server hosts or caches these translations, in the case where they are hosted the name server is often called a DNS Server.

Counting all name servers is a bit tricky, because you can't simply enumerate all the domains.

Let me give you an example on resolving superuser.com in a non-cached way:

• The name server that I use is 192.168.1.1.

  This is my local router which caches DNS entries, it has a Hosts file to reroute malicious domains.

• The router has the name servers 8.8.4.4 and 8.8.8.8 set, known as Google DNS, they also cache.

• Google DNS will contact authoritative root name servers, which are the top of the DNS hierarchy.

• Google DNS will contact the .com name servers, the IP of which it received from the ARNs.

• Google DNS will contact the DNS server for superuser.com, of which IP it received from .com.

  A simply whois reveals:

  NS1.SERVERFAULT.COM
  NS2.SERVERFAULT.COM
  NS3.SERVERFAULT.COM
  

  The IPs for these name servers are known as they are registered at the .com name server, when you register a new domain you always have to fill in the DNS servers that you use along their IP.

• Google DNS will contact the DNS servers of superuser.com to find the IP of superuser.com:

  nslookup superuser.com NS1.SERVERFAULT.COM
  Server:  NS1.SERVERFAULT.COM
  Address:  64.34.119.33
  
  Name:    superuser.com
  Address:  64.34.119.12
  

I would suggest you to read through Domain Name System and Name Servers for more details.

The term name servers are also used in different contexts, read Spiff's answer for more.

Solution 2:

Tricky!

A DNS Server typically is for converting FQDN (www.xxx.com) to IP Addresses (192.168.0.1).

(A DNS Server also does a lot more, it can perform reverse lookups, and in recent years does a lot of other tasks with text tags, geo-ip and a lot more).

On the other hand, "Name Server" is typically used to locate a DNS Server.

For example, On a Whois record, a Name Server is typically the address for the DNS server that hosts the records for that domain.

A further more complicated example is, if you queried www.superuser.com, you would go to your dns server and a recursive DNS lookup would occur on the superuser's nameserver.

As for how many are there - how long is a piece of string! This is an impossible question to answer... As a guess, I would put it in to the hundreds of thousands, if not low millions (for publicly accessible DNS Servers).