Machine Learning is not just statistics. David Donoho spells out the history of the whole thing in his 50 Years Of Data Science:
https://courses.csail.mit.edu/18.337/2015/docs/50YearsDataSc...
The clearest statement of the difference I've found is Leo Breiman's "Statistical Modeling: The Two Cultures:"
https://projecteuclid.org/download/pdf_1/euclid.ss/100921372...
The abstract has a succinct explanation:
> Abstract. There are two cultures in the use of statistical modeling to reach conclusions from data. One assumes that the data are generated by a given stochastic data model. The other uses algorithmic models and treats the data mechanism as unknown. The statistical community has been committed to the almost exclusive use of data models. This commitment has led to irrelevant theory, questionable conclusions, and has kept statisticians from working on a large range of interesting current problems. Algorithmic modeling, both in theory and practice, has developed rapidly in fields outside statistics. It can be used both on large complex data sets and as a more accurate and informative alternative to data modeling on smaller data sets. If our goal as a field is to use data to solve problems, then we need to move away from exclusive dependence on data models and adopt a more diverse set of tools.
The "stochastic data model" camp covers most of what people think of when they think of traditional stats -- everything from OLS through to more sophisticated techniques. Things like neural networks and random forests are algorithmic techniques that make no assumptions about or conclusions about the distribution of the underlying data.