It’s reference points. Their axis of rotation is not the same, and more importantly, they are spheroids, not cylinders, so a significant wobble can occur at times as the flow becomes unstable.
Exactly. I think it highly unlikely that there's a sharp delineation between a "solid spheroid" inner core and an enclosing "viscous liquid" outer core. I.e. it's probably not like a billiard ball in a bag of pudding, but more like a lump of chocolate in a bag of chocolate that has softened. And as you say, the axes of rotation are very likely skewed.
The idealized drawing is just a simplified artist's conception. Nothing is that clearly defined in reality.