There was a word “nitpicking” in sanahtlig’s last post before edited, which perfectly describes what you two have been doing, possibly that’s why he removed it.
I didn’t bother with your first part cuz this gonna be stating the obvious, but if you insist:
First of all, classifying KHs is a simplification of the complexity of their ability composition, thus I started that paragraph with “In general”.
Atk down, surely it’s a debuff, along with def up, are typically of defense style, e.g. Joan.
Healing and cleanse are healers’ abilities.
Def down, affliction and gauge manipulation are debuffer’s skill, who usually classified as Tricky type in-game, e.g. Mordred.
After all this is just terminology, if you still got different opinions, be my guest.