I consulted a colleague who is well-versed in both statistics and ML to get a second opinion on the broader question and they had the following nuanced summary :

Statistics and machine learning are not mutually exclusive (in other words, most “machine learning models” are also “statistical models”). However, as modern companies (and other entities) collect more and more data and want to analyze/leverage it, data scientists/statisticians/people-who-work-with-data have reached some of the limitations of traditional statistical methods and models. Luckily, advances in computer science and technology have enabled researchers to discover new algorithms and methods for fitting these models. When people use terms like “machine learning” and “data science” they are often referring to these newer algorithms, but the truth is that it’s all a natural extension of statistics to leverage advances in computer science and deal with big data (and a more diverse set of questions/goals).

That said, some people like to make a distinction between data analysis and predictive modeling/machine learning. Many statistical/ML models can be used for both purposes. For example, a linear regression model could be used to predict the amount of money that a particular customer will spend at a restaurant. In this context, it is a “machine learning model” because we are using it to train a computer to predict how much money someone will spend without explicitly telling the computer how to make that prediction. However, the same model can also be used to figure out (“analyze”) which customer attributes are most associated with spending. In that context, we might think of the regression model as a “data analysis technique”. However, the truth is that this step (of inspecting the model and understanding how it works) is an important part of machine learning/prediction anyways (to figure out ways that the model/data might be biased/inaccurate), so it’s kind of silly to try to draw lines in the sand.