What is the difference between causal models and directed graphical models?

or:

What is the difference between causal relationships and directed probabilistic relationships?

or, even better:

What would you put in the interface of a DirectedProbabilisticModel class, and what in a CausalModel class? Would one inherit from the other?

Collaborative solution:

interface DirectedModel {
  map<Node, double> InferredProbabilities(map<Node, double> observed_probabilities,
                                          set<Node> nodes_of_interest)
}
interface CausalModel: DirectedModel {
  bool NodesDependent(set<Node> nodes, map<Node, double> context)
  map<Node, double> InferredProbabilities(map<Node, double> observed_probabilities,
                                          map<Node, double> externally_forced_probabilities,
                                          set<Node> nodes_of_interest)
}