There's a 3rd factor: memory. I.e. a somewhat static NN can still make input/output to more dynamic memory. E.g. you could have basic feature detection (edges

There's a 3rd factor: memory. I.e. a somewhat static NN can still make input/output to more dynamic memory. E.g. you could have basic feature detection (edges or maybe even something relating to facial features) prebaked into your visual system. General object categorization gets learned by the visual system while recognizing locations where you have been before needs to access memory. Of course in the human brain memory is just another big web of neurons with different tradeoffs, but in software you can use other things.