How to tell an armature action from a model action?

Apparently, you can associate actions with models or armatures (or both)… but the Blender UI doesn’t really reflect this clearly?

Especially, if you managed to mess up your action associations and want to get back to “regular” animation, you can end up with this when you try to add a keyframe:


I tried looking at various videos online, but none I’ve seen so far even mentions “armature actions” vs “model actions” (and few do anything more than basic action re-assignment).