As far as you’re concerned, a Category Moderator is a category moderator. After all, the clue is in the name! duh! They moderate categories! However, the concept of a category moderator happens to be alien to me and the distinguishing characteristic of a category moderator is the permissions, not the category quality. This is why me saying:
appears to you to be me missing the obvious but it isn’t.
Is there a reason a category moderator can’t have Moderator permissions? Referring back to your original image; I infer that Test_Two has Moderator permissions, it’s irrelevant to me that “General” happens to be written adjacent. As far as I’m concerned, that is an informal “You look after this category Test_Two.” How does one know otherwise?
Category Moderator is a proper noun in Discourse, as is Moderator. In my opinion, labeling a Category Moderator a Moderator is to mix up two concepts. What is the point of giving something a name if you aren’t going to stick to your own parlance? Or to put this another way; leave /about as is and instead put TL0, TL1, TL2, TL3, TL4, Moderator, Moderator here. Doesn’t make much sense does it! 
And I don’t understand why /about is different.
Pretty nuanced difference that takes some effort to understand in my opinion. Although it is It isn’t mentioned in the permissions page mentioned in my first post!
The second image doesn’t improve on the issues I feel are there, however, if the feeling is the way things are is the right way, that’s fair, perhaps the conceptual difference between Moderator and Category Moderator could be communicated?