https://www.nature.com/articles/nmeth.4642

This article use different wording than me, but in essence: Statistics is mostly about using a known model to explain the data. Machine Learning is mostly about finding any model that predicts the data well. Different purposes with some overlap. Some statistical methods are used in Machine Learning, but that doesn’t necessarily mean all of Machine Learning is statistics.

The boundary between statistical inference and ML is subject to debate—some methods fall squarely into one or the other domain, but many are used in both. […] Statistics requires us to choose a model that incorporates our knowledge of the system, and ML requires us to choose a predictive algorithm by relying on its empirical capabilities.

Another (potentially lower quality) article that is not from Nature, but discusses the meme in particular:

https://www.datarobot.com/blog/statistics-and-machine-learning-whats-the-difference/

Because of the large number of variables in machine learning datasets, the models developed from them can be simultaneously extremely accurate and almost impossible to understand. Statistical models, on the other hand are typically easier to understand because they are based on fewer variables, and the accuracy of relationships is supported by tests of statistical significance.