There are many duality theories in mathematics where both of these perspectives are valid. Each instance is "Duh! What's going on here is just..." and the pragmatic move nimbly through each instance without concern. For others, the potential theory IS the object of interest. Is this apparent pattern a deep principle or just a mirage? When something is actually going on, one learns powerful new techniques by recognizing a precise pattern.

I've stumbled onto deeply disguised dualities in my career. (One could argue with a straight face there are only two, but this is not formalized.) It's more a psychological process than a technical one.

It's always possible to ignore that one is standing in a tree farm. Trees have such interesting bark.