What is a TOP Level Domain Name?
The last component of a domain name, for example the domain yourbusiness.com has a top level domain of com. TLD's are the names at the top of the DNS naming hierarchy. They appear in domain names as the string of letters following the period such as "com" in yourbusiness.com>/b>. Some common TLD's include .com, .net, .org, .gov, .edu etc.

If you had a web address such as http://www.goldenwest.net/~username, that would NOT be a top level domain. It would be a page under the top level domain.

What is a Third Level Domain?
In a domain name, that part of the domain name that appears two segments to the left of the first level domain.

Third Level domain names are also known as sub domains or canonical names. The Third Level, unlike a domain name, is not registered anywhere because it is associated with a domain name. It is created by the Web Host on the DNS server.