I do not see these words used interchangeably, but they seem to be similar. In inverse modeling we are trying to find causal factors given an effect. In causal discovery, we are also looking for causal factors, right? How would you use these terms in different situations?
Topic causalimpact correlation graphs statistics data-mining
Category Data Science
A similar question could also be "What is the difference between Bayesian Network learning and causal discovery?". I'm portraying the problem this way because causal networks can be [causal] Bayesian Networks, which makes the question even trickier. What is the difference then?!
The goal of causal discovery is to reconstruct a causal graph from data, as compared to the goal of Bayesian Network learning that is to reconstruct a probabilistic graphical model (PGM) from data. The difference here are the assumptions that are used, and the interpretation given to the network.
$ A \rightarrow B \rightarrow C $ in a Bayesian Network does not mean $A$ is a cause of $B$, but that is the interpretation if it's a causal network. The set of assumptions used, among other things, will convince others [or not] that this causal relationship is reasonable.
Causal Discovery is usually more worried about direct relationships and relationship orientations than other common network inference approaches. One way of putting it is that causal discovery is a subset of inverse modelling.
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