Machine learning is a subset of AI. That is, all machine learning counts as AI, but not all AI counts as machine learning. For example, symbolic logic – rules engines, expert systems and knowledge graphs – could all be described as AI, and none of them are machine learning.
One aspect that separates machine learning from the knowledge graphs and expert systems is its ability to modify itself when exposed to more data; i.e. machine learning is dynamic and does not require human intervention to make certain changes. That makes it less brittle, and less reliant on human experts.
"A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P if its performance at tasks in T, as measured by P, improves with experience E." --Tom Mitchell
In 1959, Arthur Samuel, one of the pioneers of machine learning, defined machine learning as a “field of study that gives computers the ability to learn without being explicitly programmed.” That is, machine-learning programs have not been explicitly entered into a computer, like the if-then statements above. Machine-learning programs, in a sense, adjust themselves in response to the data they’re exposed to.