I think Procida initially created this as part of their work with Divio and then forked it to the Diataxis site. The Divio site was definitely around before Diataxis and the Divio site was where these ideas originally gained a lot of popularity.

They’re officially related. Personally, prefer the link I used since it provides a table of contents and link to this YouTube presentation on the system:

https://m.youtube.com/watch?v=t4vKPhjcMZg

This variant seems worse than the dataxis one.

It's already a weakness of this "theory" that it leaves only the reference for documentation that's intended to be complete and correct, while also recommending that the reference be organised as a list of the available operations.

But this divio variant goes so far as to say that, when writing the reference, "don't allow explanations of concepts".

I believe good documentation often needs rigorous definitions of the concepts involved, not just a list of functions or configuration items or whatever.

So either the reference should have space for those, or the explanation should be in a more rigorous style, not a "more relaxed" discussion.