fwiw, alreq these days refers to this kind of thing as 'writing styles' (see https://w3c.github.io/alreq/#h_writing_styles)

correct, those should not be called as "typefaces". "Writing styles" is good for me.

But wasn't Fangsong a specific type of type face following the characteristic of certain calligraphist from ancient time that follow the writing style of his time?

https://www.w3.org/International/articles/typography/fontstyles.en.html and https://www.w3.org/TR/typography/#fonts use the term "font styles".

Just a note on that. Alreq continues to use the term 'writing styles', but it seemed to me when i wrote the article that 'font styles' felt more intuitive, so i used that term. It does, of course, need to be distinguished from the CSS concept of 'font-style', but i thought it still worked OK. I'm not aware of any industry terminology that is widespread. Titus and i had a similar discussion before settling on 'writing style' for alreq (some years ago, now).

I think "Writing style" in arabic writing is more similar to the like of Big Seal Script in CJK from various nations in warring state period, instead of the different writing types of Fangsong and such.