Answering myself, I think wikipedia might have clarified my confusion: > The study of mathematical optimization delivers methods, theory and application domain

Answering myself, I think wikipedia might have clarified my confusion: > The study of mathematical optimization delivers methods, theory and application domains to the field of machine learning. > Machine learning (ML) is the study of computer algorithms that improve automatically through experience. So it seems optimizations are the techniques for which most ML is based on, but ML is more of the idea that an algorithm would improve automatically from experience. Later in the wikipedia page, it creates a very clear distinction: > The difference between the two fields arises from the goal of generalization: while optimization algorithms can minimize the loss on a training set, machine learning is concerned with minimizing the loss on unseen samples.