It's not a technical term. Nowhere in the current HTML standard will you find a versioning of HTML. That's why it's now called a "living standard". You will never find a HTML6 or higher. That note you found is to help with any confusion.
One of the annoying things about having a living standard is that it is difficult to implement a conforming version as additional updates means that you are no longer conforming.
Versioned standards allow you to know that you are compliant to that version of the specification, and track the changes between versions -- i.e. what additional functionality do I need to implement.
With "living standards" you need to track the date/commit you last checked and do a manual diff to work out what has changed.
> You will never find a HTML6 or higher
You might be right, but we don't know yet. Microsoft said that for Windows 10.
You might also be right that the current Living Standard specification doesn't really call it HTML5, but you'll find many people writing HTML for a living say HTML5 to refer to it, and telling them that HTML5 doesn't exist doesn't really help and is a bit wrong too if you have a descriptive approach to languages.