What’s so variable about the variable oystercatcher?

Looking at this photo and knowing it’s a variable oystercatcher (Haematopus unicolor), the question that comes to mind is: What exactly is so variable about the variable oystercatcher? Its plumage is completely black, its species name is unicolor (truly!), and what’s going on with those orange chopsticks strapped to its face? As with the fantail, there are different colour morphs, but unlike the fantail, it’s not simply a matter of “black” or “pied” and nothing in between. The colouring is much more, well, variable, ranging from the completely black in this photo through to a half-singlet wearing pied morph. And in between, there are “smudgies”, with varying degrees of white. All have the orange chopsticks and the red eye ringed with orange.