Semantic Elements and Text Formatting in HTML5

Almost every website, book, article, newspaper, etc... that contains copyrights, caveat, disclaimers, etc... displays it in small font text.

Now... I'm doing a research about Semantic Elements and Text Formatting in HTML5, and we know that we should use <strong></strong> instead of <b></b>, for example, if we're not just styling the content to display bold text, it's about how important is the text, because at the end of the day, HTML elements present the "data" that it includes, and if we just want to give the text an attention, we should avoid using <b></b> and use <span></span> and style it in CSS, because that's the usage of CSS - styling.

Since the <small> element is semantic, it leads us to the question:

Why the font of these information are displayed, usually, in small size?

I'm trying to understand why <small> is a semantic element.