In addition to Mike Hunter's excellent answer (+1), I'd like to point out the envisioned application fields of statistics, contrasted to Machine Learning.
Statistics was historically developed as a tool for informing human decision makers about dependencies in social and physical phenomena. Humans would analyse the statistical findings, consult, debate and, eventually, after a lot of deliberations, make a decision. Statistical analysis comes with a load of "ifs" and "buts" and is just a help to human experts.
Machine learning, on the other hand, evolved from attempts to allow machines make autonomous decisions, ideally without human help at all once the training process has been completed. The internal representation of what the machine has learned is not intended to be human-readable and an analysis of the findings is seldom possible.
As an example, think of economics vs. stock trading. If you were an economist in a national bank, you'd statistically analyse data regarding the country's economy (unemployment, inflation, GDP etc.) and, after a lot of deliberations and consultations with your peers, decide whether to rise the interest rates or not. Statistics is here a tool helping the expert make an informed decision.
At the stock market, in contrast, you want to react as soon as possible, in some cases even within milliseconds, to market changes. You don't have time to ponder and discuss. Either you trust your experience and gut feeling, or you leave the decision to a suitably trained machine.
Another example is traffic: Statistics might be useful to design a road network and traffic signalling, but, once on the road, p-values and confidence intervals are useless. You either drive yourself, based on what you've learned and your experience, or you let a self-driving car drive you. In both cases, you make no use of statistics.