What distinction is there between statistical inference and causal inference? Be it on a practical or theoretical level, what would you say are the key differences between statistical inference and causal inference.
I've been trying to learn more about causal inference and don't see a key difference in most instances.
If anything, I'd say that statistical inference is about finding associations, while causal inference uses counterfactuals/dag's to infer causal patterns. So there are differences in terms of techniques and a greater emphasis on things like omitted variable bias.
 A: Causal inference is the process of ascribing causal relationships to associations between variables.  Statistical inference is the process of using statistical methods to characterize the association between variables.  Causality is at the root of scientific explanation which is considered to be causal explanation.  However, establishing causal relationships is extremely difficult in spite of substantial advancements made during the past decades.  Statistical inference works like a black box and generates the best possible characterization of the relationships between variables.  Statistical inference provides estimates of the associations between variables but of course, association does not imply causation, so there is little that statistical inference can provide to establish causation.  That is not to say that statistical tools cannot be used to establish causal relationships but for that purpose a number of rules must be taken into account.  These rules are what is generally known as the covering laws of which statistical inference is the method used in the model of statistical relevance designed to establish scientific explanations.  As scientific explanations are causal explanations a delicate relationship is established between statistical inference and causal inference.  For a review of these concepts see Judea Pearl's "Causal inference in statistics:An overview" (http://ftp.cs.ucla.edu/pub/stat_ser/r350.pdf).  
A: "Causal inference" mean reasoning about causation, whereas "statistical inference" means reasoning with statistics (it's more or less synonymous with the word "statistics" itself). So, causal inference is a subset of statistical inference, except that you can do some causal reasoning without statistics per se (e.g., if event A happened before event B, then B cannot have caused A). The inverse definitely doesn't hold because many statistical methods have nothing to do with causation, and can be fruitfully applied in situations where the data permits no causal inferences.
A: Causal inference uses techniques like 
matching before fitting statistical models. In other words, causal inference puts more emphasis on research design, while statistical inference puts more emphasis on the mathematical/computational part.
