domain that is directly below a top-level domain
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What is the difference between the third level domain and SLD?
How do SLDs differ across various domain extensions)?
How do SLDs relate to domain registrars?
Just count the dots...
.co.uk is a top level domain aka first level domain;
uk is a TLD. co is a SLD.
(Reference: http://www.nominet.uk/uk-domain-names/about-domain-names/uk-domain-family)
Although it's common to see .co.uk described as a ccTLD, it's really only the uk part that is the TLD.
google.co.uk is a second level domain and an apex domain;
google is a third level domain.
And now the hard part: .name domains
...Just count the dots.
You seem to confuse the technical definition with registration policies.
.co.uk is not a TLD. .uk is a TLD. As w3d notes, "just count the dots".
But .co.uk is "special" in the way that you may register your domain name under this second-level domain. It’s an effective top-level domain (eTLD).
Mozilla hosts a list of these eTLDs, which they call Public Suffix List. They define a public suffix like this:
A "public suffix" is one under which Internet users can (or historically could) directly register names. Some examples of public suffixes are
.com,.co.ukandpvt.k12.ma.us. The Public Suffix List is a list of all known public suffixes.