Difference between Stencil -structures and Cellular Automata Category-theoretically?
Judging from the source you provided, there appear to be two key differences:
(1) stencils have numeric values in each cell and update the cells with functions defined numerically (typically using continuous functions) while cellular automata typically have only a finite set of values per cell and use functions that in general do not arise from numerical methods, and (2) stencils are updated by a sweep across the grid while in cellular automata generally all cells are updated simultaneously.