This goes back to printer terminology which was heading, then subheading, then sub-subheading converted to h1, h2, h3 but initially as in printing it was defined by size and boldness of the print. Then there was a need to tell search engines something besides showing bold font in various thicknesses. So as to sort the two messages, one to search engines and one to readers, the h tags were defined to talk to the search engines in terms of the what was the heading, what was the subheading and what was the sub-subheading, as compared to visually showing the viewer something.

The h tags should be considered as talking to search engines and not so much to inform the viewer. 

Another way to approach this is to consider if I bold just one word in a sentence. What am I trying to say to a viewer by doing that and what does the computer do with that in terms of querries from search engines?

So if I use the em tag (emphasis), the search engine gets a notation, that this is something I emphasize for some reason but the viewer may see that in a different way as some boldness in 300, 300, 500 or more.

I think to understand what they did, one has to know that they wanted to talk to the search engines and also convey the author’s stress to viewer but keeping the search engines properly informed.

For instance, you can put an h1 tag and that will come up to the viewer as just a large bold font but to the search engine that is the heading of the article or whatever. But if you add some CSS to that h1 tag, you can make it so that it is an elephant size of font and you could even remove all bold features from it, and still the search engines will regard it as heading because it is h1 but viewers will regard it differently because it was not bolded. They may only read it as an artistic type of font and not even bother to note that it is a heading.

Let us say that I have a heading and I bold it only and use just p tags (paragraph), then viewers will see that as bolded and may interpret it as the heading but the search engines will ignore that because it has a p and not an h tag.

This is clear when you use a program like Microsoft Word to compose text, where if you use a p tag, it will be regarded as ordinary text and then when you try to create a Table of Contents, using Word to compose that, your headings which were in a p tag will not show up, unless you open the paragraph dialog and change the p tag to an h tag, by telling the system in the outline level to change from Body Text to Level 1, Level 2 and so on.

It is reduced to making a decision as to what you want to say to the search engines and what you want to say to readers and knowing how to do that using the html tag system. It took me a while to get used to this. I got over 30 books now and had to figure this out at first using Microsoft Word and then converting plain text to html in preparation for making ePub files. It requires a new way of thinking about text or even images, where the intruder is the search engines. 

How to inform both the human viewer and the search engines (AI viewer) at the same time? That is the skill to acquire.

well put Michael Beloved couldn't have put it better myself