I think it’s actually both important and possible to differentiate between stats and ML (and AI for that matter). Statisticians, ML engineers, and data scientists all have related but distinct skill sets, knowledge, methodological experience, and worldviews. The identification can be important because it suggests what sorts of tasks and projects an individual is well-suited for. (Notwithstanding the fact that I believe anyone can acquire skills/knowledge to be competent at any of those jobs and transition between them with a bit of effort).
For example, consider the work that the FDA does in evaluating clinical drug trial data. In this case, you need statisticians on staff that can critically analyze the statistical/methodological rigor, not to mention understand the medical domain and relevant regulations/processes. It doesn’t matter if they can only use the GUI versions of SAS and have never heard of TensorFlow, their time is better spent deeply understanding nuances of experimental design, sampling methods, causal analysis, estimation, etc. I would argue that a “good” statistician in this context might very well be “not so good” at data analysis, as long as they can clearly and accurately critique experiments and analyses and identify when things go wrong. Also consider—what would happen if you slotted a ML engineer into a role like this?
ML engineers are best at optimizing performance (not just accuracy) at some defined task, where ideally the cost of the model being wrong in some exotic way is not astronomical (e.g. approving a dangerous drug, convicting an innocent person, initiating a stock crash, corrupting the attention span of the human race). A good use case for machine learning comes from the book Pattern Recognition—sorting fish on a conveyor belt. No one gives an ounce of chum about statistical rigor in this case, and the consequences of being inaccurate are quantifiable and manageable. But building and tuning a ML system to do this at an acceptable performance level requires a ton of work. You’d need to define the sensor array / inputs, collect and label data, engineer features (more relevant before deep learning, in the case of computer vision), train and evaluate an object detection model, avoid overfitting the training data, build an anomaly detector to weed out the stray crab, ensure it works fast enough to be used in production, turbo-browse arXiv to make sure your stuff isn’t obsolete (damn, it is). This is a vastly different focus than statisticians, who wouldn’t get very far with this sort of performance-optimization problem.
Data scientists are somewhere in between a statistician and ML engineer—like a hybrid class in an RPG. They can cast a few key ML spells and have dabbled in arcane math, but can also slice up data goblins by hand (maybe even with style). With a foundation in a bit of everything, they can glue a team together and flexibly grow in multiple directions. But they can also become a waste of shiny gold if pitted against a specialized task without support from, you know, specialists.