The best distinction I've found between ML and statistics is the following.
Statistics is about modelling the underlying probability distribution that generates your data. A convergence/generalization/etc result will usually be dependent on this underlying distribution.
ML is when you don't care much about the underlying distribution (modulo regularity assumptions), and your model doesn't even come from the same family at all.
I.e. linear regression is usually statistics, because you often believe the underlying data looks like f(x) ~ f(x0) + f'(x0)(x-x0)). Random forests are machine learning because you don't actually think the real world secretly has a random forest flotaing around.
Statistics is about modelling the underlying probability distribution that generates your data. A convergence/generalization/etc result will usually be dependent on this underlying distribution.
ML is when you don't care much about the underlying distribution (modulo regularity assumptions), and your model doesn't even come from the same family at all.
I.e. linear regression is usually statistics, because you often believe the underlying data looks like f(x) ~ f(x0) + f'(x0)(x-x0)). Random forests are machine learning because you don't actually think the real world secretly has a random forest flotaing around.