Do note that the existing name in the CS literature for algorithms that can cheaply provide an "updated" result given a change in the input is dynamic, not differential. "Differential" actually refers to something else altogether, namely being able to automatically compute the gradient of some general calculation on continuous-valued inputs! (The intersection of differential and dynamic problems, where the point is to recompute answers quickly when some continuous-valued input changes, is called "kinetic".)

"Incremental" is actually a special case of dynamic, where all updates are restricted to 'adding' input data only. (Thus "incremental" algorithms, properly understood, are closely related to "online" algorithms, e.g. those which process input data in a streaming fashion as opposed to assuming a "complete" input to begin with.)