The difference between Statistical Modeling and Machine Learning, as I see it

The basic goal of Statistical Modeling is to answer the question, "Which probabilistic model could have generated the data I observed?" For example, if your data represent counts, such as the number of customers churned or cells divided, then a model from the Poisson family, or the Negative Binomial family, or a zero-inflated model might be appropriate. Once a statistical model has been chosen, the estimated model serves as the device for inquiries: testing hypotheses, creating predicted values, measures of confidence. The estimated model becomes the lens through which we interpret the data. We never claim that the selected model generated the data but view it as a reasonable approximation of the stochastic process on which confirmatory inference is based.