[jahewson]

What makes dynamic programming special is that it exploits optimal substructure, where a problem can be broken down into smaller sub-problems, the solution to which must be part of the optimal solution to the larger problem.

While caching can be applied anywhere, dynamic programming can only be applied where optimal substructure is present. For example, finding the shortest path between all points in a graph. Likewise, finding the longest path doesn't have optimal substructure and so dynamic programming cannot be applied in that case.