"Differentiable" describes some computation for which derivatives can be computed. "Differential" is a more general term which means that something has to do with differences, e.g. differential equations deal with equations that specify how things change together.
With the recent surge in deep learning came significant improvements in optimization techniques and hardware, making it feasible to formulate some computations in a differentiable manner. Doing that allows one to optimize the computation process relatively efficiently, at least in theory. Some other examples: differentiable programming (other differentiable techniques are a subset of this), differentiable rendering, differentiable signal processing.
For instance edge detectors and even most feature detectors are basically hard-coded kernels, are they not? And you wouldn't apply them on intermediate representations, they are only really valid operations for the input layer, and not needed during back-propagation.
I find the examples interesting, but mostly are things that could be done using OpenCV and don't exploit the differentiability in any meaningful way. But maybe I am missing something.