If that set of labels doesn't work for you, there are many other ways that the Diataxis doc attempts to explain the differences. You might find it a useful exercise to seek terms that make more sense to you. Or just to try to understand them in other ways - e.g. via the action/cognition ("do vs. think") and acquisition/application ("at study vs. at work") dichotomies.
There's an entire page devoted to distinguishing tutorials from how-to guides (https://diataxis.fr/tutorials-how-to/). (Note that this is itself classified as "understanding" material; as an exercise, you could try to evaluate the writing there to see how it maps onto what is described as "explanation", and doesn't map onto how a "tutorial" is supposed to work.)
But to me, one of the simplest distinctions is that a "tutorial" is the sort of thing that you can't do on Stack Overflow. That's because a tutorial involves following a lesson plan that was set by a teacher, who fills in the student's unknown unknowns. On Stack Overflow you must ask a question; a tutorial is material for someone who doesn't yet know what to ask.
There are plenty of extraordinarily popular questions on Stack Overflow that ask how to do some simple task. But to work in the format, you have to ask, not simply request help (see also: https://meta.stackoverflow.com/questions/284236).
Their doc actually explains the difference efficiently though :
Tutorials - learning-oriented experiences
How-to guides - goal-oriented directions
Reference - information-oriented technical description
Explanation - understanding-oriented discussion
I guess that's still better than labelling them Type I-IV tutorials.
The lecture is the explanation. The tutorial/lab is a guided experience (Microsoft's fake Contoso company comes to mind). A how-to guide is what you need when you want to search/chatgpt a solution. Reference material: thesaurus, encyclopedia, owner's manual.
Video games have built-in tutorials and yet walkthrough guides are still necessary for tricky puzzles. You check the key bindings as reference.
Yes, one is focused on understanding (mechanics, lore, UI) and the other is focused on a specific task (do these steps to progress).
Diataxis is not inventing these words - it is using them deliberately. You seem unwilling to actually [learn what they mean](https://chatgpt.com/share/6751d9b7-3fd4-800a-8b81-1949069007...).