Strange, in most of the papers and the books about this they define AI and ML and their relation.
The best operational definition I got to was, it's ML when it involves a "machine" (possibly defined in software) that tries to 'optimise' some objective on behalf of a user; whereas AI involves some sort of Agent, who needs to demonstrate intelligence, that involve particular environments / states contexts, etc.
But, not everyone defines it like this. To many people AI is rapidly becoming "Neural Networks, particularly Deep ones", with ML becoming "Anything that is in scikit learn that isn't a neural network". Which isn't really a useful definition if you ask me.
1956 (or 57) the perceptron was made. The public mood was ecstatic. Generals were dreaming of robot armies, finance world was dreaming of automation, and the whole world was dreaming.
1964 (or 66?) a bestselling book was AI Winter. It explained in everyday English how the whole thing was a farce (at that time). Funding dried up. It wasn't sexy to say AI anymore. So people started saying ML. For funding they were doing ML and not AI.
Nowadays it is a top down vs bottom up approach. One is AI and the other is ML (i don't know which, it doesn't matter)