What is a 'message passing method'? I have a vague sense of what a message passing method is: an algorithm that builds an approximation to a distribution by iteratively building approximations of each of the factors of the distribution conditional on all the approximations of all the other factors. 
I believe that both are examples Variational Message Passing and Expectation Propagation. What is a message passing algorithm more explicitly/correctly? References are welcome.
 A: Maybe the article on belief propagation will be helpful. 
The article gives a two bullet point description of how "messages" are passed along edges in a factor graph. This "message passing" can be done for any graph. For trees the algorithm is exact in the sense that it gives the computation of desired marginal and joint distributions of the nodes in the tree. Iterations of the algorithm for general graphs are attempts to produce approximations of the desired marginal or joint distributions. 
A: Since you ask for references,  I can recommend chapter 16 of David MacKay's Information Theory, Inference, and Learning Algorithms. (you don't need to read the previous 15 chapters to understand ch. 16)  The book is free for downloading from the author's website (with permission from the publisher).  
For an interesting example, check out the thesis of John Winn.  Uses a message passing algorithm for generic Variational Ensemble Learning - enabling simple construction of inference problems such as ICA and PCA.
